Research ArticleStakeholder Conflict Amplification of Large-Scale EngineeringProjects in China An Evolutionary Game Model onComplex Networks

Zhengqi He 12 Dechun Huang12 Junmin Fang 1 and Bo Wang 3

1Business School Hohai University Nanjing 211100 China2Jiangsu Provincial Collaborative Innovation Center of World Water Valley and Water Ecological CivilizationNanjing 211100 China3Business School North Minzu University Yinchuan 750021 China

Correspondence should be addressed to Junmin Fang fangjunminhhueducn

Received 29 April 2020 Revised 6 July 2020 Accepted 17 July 2020 Published 5 August 2020

Guest Editor Yuetang Bian

Copyright copy 2020 Zhengqi He et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Large-scale engineering projects make tremendous contributions to Chinarsquos social and economic development meanwhile due tothe diversity of stakeholders the dispersion of time and space and the complexity of information dissemination large-scaleengineering projects are easy to cause conflicts among stakeholders that affect social stability -e previous studies on stakeholderconflicts of large-scale engineering projects mainly focused on the game model among stakeholders without considering theinfluence of stakeholdersrsquo interaction complex networks formed by social relations on the conflict amplification For the two mainstakeholders of the government and the resident that play a key role in Chinarsquos large-scale engineering projects this paperconstructs an evolutionary game model of the main stakeholder conflict amplification and analyzes the evolutionary results of theconflict between the government and the resident in different situations -e small-world network is chosen as the complexnetwork type of the simulation study since it is very similar with the topology of the realistic social network Based on the NetLogosimulation platform the stakeholder conflict amplification process of large-scale engineering projects on the small-world networkis analyzed and relevant managementmeasures are proposed to defuse the stakeholder conflict of large-scale engineering projectsBy using the evolutionary game model on complex networks this paper studies the stakeholder conflict on the small-worldnetwork providing reference for stakeholder conflict management of large-scale engineering projects in China

1 Introduction

It is generally believed that large-scale engineering project isinitiated by the government along with many stakeholdersinvolved in during the planning and implementation It hasthe characteristics of large investment scale many factorsinvolved wide range of influence and so on which hassignificant and far-reaching impact on regions and even thewhole country [1 2] As one of the most important drivingforces for Chinarsquo economic growth the construction oflarge-scale engineering project has made tremendous con-tributions to Chinarsquos economic and social development andit is also an important means and tool for stable growth andmacrocontrol in Chinarsquos central government and local

government In recent years large-scale engineering projectssuch as large water conservancy and hydropower projectslarge-scale energy projects and transportation infrastruc-ture projects start to construct in succession Takingtransportation infrastructure projects as an example threehundred and three programs had been highly promotedfrom 2016 to 2018 with an investment scale of 47 trillionRMB -e large-scale engineering project is a complexsystem with multisubjects and multiprograms and themanagement decision environment of which faces manychallenges such as spacious dispersion stakeholder diversityand the complexity of information dissemination coveringthe ldquotroikardquo that triggered group incidents land acquisitionand demolition labor disputes and environment pollution

HindawiComplexityVolume 2020 Article ID 9243427 17 pageshttpsdoiorg10115520209243427

-e conflicts caused by large-scale engineering projectshave become an important realistic problem that Chinaurgently needs to solve In the report of the 19th NationalCongress of the Communist Party of China the CPCpointed out that it should ldquofirmly fight the hard battle againstmajor risksrdquo and proposed that it should ldquostrengthen theconstruction of mechanisms for preventing and resolvingsocial contradictionsrdquo Undoubtedly the amplification ofstakeholder conflicts in large-scale engineering projects isalso a major risk and with the interest relations of someinterest groups not been properly dealt with the prominentsocial contradictions will appear resulting in various socialconflicts such as group incidents and thus leading to thedisorder of the social systems -e large-scale engineeringprojects have the characteristics of stakeholder diversifica-tion which includes not only the internal multisubjects ofproject management such as the government project legalpersons and contractors but also the external multisubjectsof project management such as land acquisition and de-molition scholars and social organizations -e mainconflicts include internal multisubject conflicts internal andexternal crossed conflicts and external multisubject con-flicts In the context of Chinarsquos special social transformationsocial conflicts triggered by the large-scale engineeringprojects occurred frequently such as Sichuan HanyuanIncident Chongqing Wanzhou 1018 Incident YunnanSuijiang 325 Incident Nantong Drainage Project GroupEvent and Sichuan Shifang 72 Incident and all of whichwere caused during the project construction -e large-scaleengineering projects have always been the focus of socialconcern all over the world and thus social conflicts are easyto occur if problems caused by large-scale engineeringprojects are not handled properly [3] -e amplification ofthese conflicts will not only affect the progress of the projectbut also may lead the project to be eventually cancelled [4]At the same time it will also have certain impact on socialstability and affect the harmonious development of socialeconomy [5]

2 Literature Review

From the perspective of the scale and complexity projectscan be divided into three levels of large medium and smallamong which the large-scale engineering projects are thelargest and most complex At present there is no consen-sus on the specific classification criteria for large-scale en-gineering projects Flyvbjerg [2] believed that with thedevelopment of economy the investment amount of large-scale engineering projects should reach at least one billiondollars Hu et al [6] studied the classification criteria forinvestment quotas of large-scale engineering projects inEuropean countries the United States South Korea Chinaand other countries thinking that a project with an in-vestment quota of 001 of the total national GDP can beconsidered as a large-scale engineering project In Chinathere are many projects that exceed these standards Forexample the total investment amount of the Beijing-Shanghai high-speed railway project reached 220 billion

RMB and the total investment amount of the South-to-North Water Transfer Project reached 500 billion RMB

Due to the development of social economy the scale oflarge-scale engineering projects is getting larger and largerand thus more and more participants are involved in theconstruction such as the government project developerscontractors constructors nearby residents relocated resi-dents and general public are considered to be stakeholders[7ndash9] -e structure of relationships among them becomesmore andmore complex and the conflicts becomemore andmore serious [10] One of the most important reasons is thedifference in stakeholdersrsquo interests resulting from differ-ences in stakeholdersrsquo status [11] Scholars divide the types ofstakeholders and determine their status from stakeholdersrsquoresponsibility in project management and their ranking ofrights in engineering projects [12 13] -e most commonway is to divide stakeholders into internal stakeholders andexternal stakeholders [14] and to study them separately[15 16] Traditionally it focuses more on internal stake-holder conflicts -rough a literature review and ques-tionnaire survey Awwad et al [17] studied reasons for andsolution to internal stakeholder conflicts in large-scaleconstruction projects in the Middle East On the other handLee et al [18] believe that conflicts among external stake-holders have become a more important factor affecting thesuccess of the project and by taking 22 representative large-scale public engineering projects in Korea as research ob-jects he proposes management framework of the externalstakeholder conflict

In China stakeholder conflicts in large-scale engineeringprojects are mainly reflected in the contradiction betweenthe publicrsquos interest appeals and the government and projectlegal personrsquos decisions [19] Unbalanced interests amongstakeholders may cause social conflicts leading to socialevents such as group incidents Social transformation usuallyleads to the adjustment of the interests of social memberswhich will inevitably lead to the increase in social conflictsIn recent years with the social transformation andupgrading of China there have been more and more groupincidents caused by large-scale engineering projects such asthe PX events in cities such as Xiamen Dalian and Qingdaoin China Group incident is a word with Chinese charac-teristics and the meaning of which is similar to the ldquocol-lective actionrdquo in Western sociology Although Westernscholars have not formed a consensus on its definition theyall emphasize that collective action is the action taken by akind of group for a common goal (generally to improve theirown conditions such as obtaining higher social status morematerial conditions and etc) [20 21] For collective actiontriggered by large-scale engineering projects scholarsrsquo re-search focuses on two aspects On the one hand a largenumber of scholars identify the factors that trigger collectiveaction and use social network analysis social risk man-agement framework and other methods to determine its keyfactors [5 22] On the other hand many scholars study theldquonot-in-my-backyardrdquo phenomenon of large-scale engi-neering projects [23ndash25] -e large-scale engineering proj-ects are generally beneficial to the vast majority of the public

2 Complexity

but which is often opposed by the local people -is is calledthe ldquonot-in-my-backyardrdquo phenomenon [26]

Although China has a social economic and politicalbackground that is not completely consistent with Westernsociety the research on collective actions triggered by large-scale engineering projects in China is mainly focused onfactors that lead to collective action and the phenomenon ofldquoNot-In-My-Backyardrdquo Taking the Sanmenxia Dam Projectand the South-to-NorthWater Transfer Project in China as acase study Liu et al [27] use questionnaires semistructuredinterviews and structural equation models to study thecauses of collective action in Chinarsquos large constructionprojects By systematically summarizing the NIMBY phe-nomenon and combining with the background of Chinarsquoslarge-scale engineering projects Wang [28] believes that riskperception and risk amplification are the main causes ofsocial conflicts Liu et al [23] use Chinarsquos 2500 question-naires to study whether the NIMBY phenomenon is themain reason for the resident to oppose the construction ofurban infrastructure projects in China and conclude thatdepriving the residentrsquos participation rights is the mainreason for collective action In addition many Chinesescholars analyze the evolution process of resident incidentsbased on incidents triggered by large-scale engineeringprojects and propose corresponding prevention strategiesand governance strategies [29 30]

Conflicts are caused by imbalances in interests amongstakeholders and thus coordinating the relationship amongstakeholders is the key to resolving conflicts Game theory isoften used to study the relationship among engineeringproject stakeholders and resolve conflicts [31ndash33] Baroughet al [34] study the application of prisonerrsquos dilemma andchicken game in construction projects and consider thatstudying stakeholdersrsquo relations with game theory is veryhelpful for conflict management of engineering projectsKang et al [35] construct a three-stage game auction modelto analyze the relationship between the government and thebidding in the public-private partnership projects Based onthe game theory Wu et al [36] construct a decision modelfor the conflict behavior between the owner and the con-tractor compare the results under the two different con-ditions of nonconflict and conflict and study the influencesof conflict behavior of large-scale engineering projects onproject performance -ere are already many Chinesescholars who use the game theory to study the conflictsamong stakeholders of large-scale Chinese engineeringprojects [37ndash39] but most of which are studied under ahomogeneous social network structure However the con-nections among individuals in realistic life are not com-pletely random but have complex network characteristics ofsmall world and scale-free [40 41] Based on social relationssuch as interpersonal relationships stakeholders of large-scale engineering project form a complex interactive relationnetwork with characteristics of the complex network NowakandMay [42] study the prisonerrsquos dilemma game on the two-dimensional square and by combining the complex networktheory with the game theory he proposes the space gametheory thus the evolutionary game research on the complexnetwork begins to get a lot of concern [43 44] At present

the study of evolutionary games on complex networksmainly focuses on two aspects Firstly under the specificnetwork structure the effects of different evolution rules onthe evolution results are studied such as imitating the bestrule and imitating the winner rule Secondly there are al-ready many scholars who have been made on the influenceof different network structures on the game results such asrule network scale-free network and small-world networkand [45 46] In addition many scholars have carried outtargeted research in different fields such as finance andsociety Liu and Wang [47] constructed the coevolutionmodel of social network structure and strategy according tothe topology of social network and made a case study byusing the NetLogo social network simulation platformBased on the network association structure of investors Bianet al [48] established the simulation and evolution model ofherding behavior in the stock market under the strategy ofthe coordination game in the network and studied the keyfactors that influence the change of investment behavior ofstock market investors from the perspective of the networkBased on consumersrsquo different preferences for electric ve-hicles Fang et al [49] divided consumers into three types ofstakeholders to considering the time-varying demand ofelectric vehicle charging stations and gas stations andstudied the construction of electric vehicle charging infra-structure in the evolutionary game model of small-worldcomplex networks -erefore based on the identification ofthe major stakeholders of large-scale engineering projectsthis paper builds a game model about the evolution ofstakeholder conflicts amplification carries out simulationresearch on complex network to explore the impacts offactors such as complex network characteristics on the resultof evolutionary game

3 Evolutionary Game Model on StakeholderConflict Amplification in Large-ScaleEngineering Projects

31 Model Hypothesis Although there are many stake-holders in large-scale engineering projects including gov-ernments project developers contracts constructorsnearby residents relocated residents and general publiconly some of which play a key role in different problems Forthe social conflicts and social stability risks caused by en-gineering projects the stakeholders who play a key role areusually the core stakeholders such as the governmentproject developers and the resident [8 9 50] In Chinalarge-scale engineering projects are generally led by thegovernment while project developers undertake specifictasks such as project planning fund raising and con-struction implementation Especially for the handling ofsocial conflicts such as resident incidents it involves thebasic interests of the resident and the governmentrsquos emer-gency management capabilities which is mainly a gamebetween the government and the resident During thisprocess project developers mainly assist in relevant work ofthe government departments Most of Chinarsquos current large-scale engineering project conflict research studies group

Complexity 3

event evolution research studies and other related researchstudies are based on the game between the government andthe resident For example Liu et al take the urban demo-lition group events as the research object and take thegovernment and the resident as both sides of the game tostudy the conflict evolution of the urban demolition groupevents [29] Song and Liu [51] constructed a game modelbetween local governments and protesters and studied themechanism of resolving group events Based on existingresearch this paper considers the actual situation in Chinahighlighting the key stakeholders in the group events causedby large-scale engineering project conflicts On the otherhand this paper considers the complexity of the modelsimplifying the model so that the conflict evolution processand results can be shown more clearly -erefore this papermainly considers the government and the resident as bothsides of the evolutionary game -e basic hypothesis of theevolutionary game model of the stakeholder conflict am-plification is as follows

(1) In the evolutionary game model the two partici-pating groups are the resident (A) and the govern-ment (B)

(2) When related conflicts occur in large-scale engi-neering projects the resident has two strategies ofrational negotiation and violent resistance namelythe strategic space of the resident isSA rational negotiationA1 violent resistanceA21113864 1113865Moreover due to the differences of the local peoplein social and economic status and social relations theattitudes toward large-scale engineering projects arealso different-e resident take decentralized actionsin the strategic space rational negotiation1113864

A1 violent resistanceA2 Most people understandthe construction of large-scale engineering projectsand choose rational negotiation while some smallparts take excessive behavior for violent struggle-is hypothesis also conforms to participantsrsquo con-ventional behaviors in the evolutionary game and asmall part of the participants adopts hypothesis ofattempting behavior by the trial-and-error method

(3) Due to differences in governance concepts politicalachievements and support degree for large-scaleengineering projects there are two strategies ofcompromised acceptance and tough control in re-sponse to the reaction of the resident namely thestrategic space of the government which isSB compromise acceptanceB1 tough controlB21113864 1113865In this game the government will be affected byhigher-level governments and public opinions thusthe strategies adopted will be constantly adjusted

(4) According to the governmentrsquos relevant guaranteesand interest compensation the resident will makedecisions of rational negotiation or violent resis-tance which is in line with the ldquomyopiardquo hypothesison the decision of evolutionary games -e residentwill observe the benefits with corresponding deci-sions made by the people around them as a reference

for their own decisions Similarly when the gov-ernment responds to the reaction of the resident itwill also make strategic adjustments on the basis ofthe situations of the previous round

32 Dynamic Evolutionary Game Flow and Replication Dy-namic Equation -e specific game flow of the stakeholderconflict amplification and evolution in large-scale engi-neering projects is shown in Figure 1 which is mainly di-vided into two stages In the first stage when conflict issuesoccur the resident should either support the project andadopt rational negotiation strategy for their own relateddemands (namely A1) or they do not understand theproject or worry that the project construction will affect theecological environment and their own interests thusadopting violent resistance strategy for their own relateddemands (namely A2) When facing different strategies ofthe resident the government either chooses compromisedacceptance strategy (namely B1) or tough control strategy(namely B2)

Before the implementation of large-scale engineeringprojects the resident and the government have certainretained earnings which are respectively recorded as RA

and RB If both parties adopt moderate strategies (the res-ident adopts rational negotiation strategy and the govern-ment adopts compromised acceptance strategy) theincreased total revenue caused by the large-scale engineeringproject is R and the proportion of the resident is α(0lt αlt 1)-e total cost paid during the moderate negotiation processbetween the two parties is C and the share proportion of theresident is β(0lt βlt 1) Generally speaking large-scale en-gineering projects have a greater role in promoting localsocial and economic development so we believe that RgtCWhen the resident adopts rational negotiation strategy andthe government adopts tough control strategy neither partycan obtain the increased revenue from the large-scale en-gineering projects Due to the attempt to adopt negotiationstrategy the resident will still need to pay the correspondingcost under mild negotiation Because the government adoptstough control strategy and does not need to bear the costunder a moderate negotiation state it needs to increase themaintenance expenditure ΔS for the tough control In theprocess it also gets the additional income ΔRB from theproject When the resident chooses the violent resistancestrategy and the government chooses compromised accep-tance strategies the resident needs to bear the cost of violentresistance ΔL but they will also receive additional com-pensation ΔRA from the project At this time as the gov-ernment tries to adopt the compromised acceptancestrategy and it needs to pay the corresponding cost underthe mild negotiation When the resident chooses violentresistance strategy and the government chooses the toughcontrol strategy both parties should undertake extra cost ofviolent resistance and maintenance expenditure for theirstrong attitude but at the same time they can also getadditional income and interest compensation from theproject -e payoff matrix of the evolutionary game between

4 Complexity

the resident and the government of the large-scale engi-neering projects is shown in Table 1

Assuming that the proportion of rational negotiationstrategy A1 adopted by the resident is x and that of com-promised acceptance strategy B1 adopted by the governmentis y the expected revenue of rational negotiation strategy A1and violent resistance strategy A2 adopted by resident arerespectively

UA1 yαR + RA minus βC (1)

UA2 RA + ΔRA minus ΔL (2)

-e expected revenue of the compromised acceptancestrategy B1 and tough control strategy B2 that the gov-ernment adopts are respectively

UB1 x(1 minus α)R + RB minus (1 minus β)C (3)

UB2 RB + ΔRB minus ΔS (4)

It can get that the expected revenue of the resident andthe government is respectivelyUA x yαR minus ΔRA minus βC + ΔL( 1113857 + RA + ΔRA minus ΔL

UB y x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 + RB + ΔRB minus ΔS

(5)

It can further get that the replicated dynamic equationsof the resident and government are respectively

dx

dt x(1 minus x) yαR minus ΔRA minus βC + ΔL( 1113857 (6)

dx

dt y(1 minus y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 (7)

In can be known from formula (6) that when x 0 1 or

y ΔRA + βC minus ΔL

αR (8)

the resident can achieve partial stability by adopting therational negotiation strategy from formula (7) when y 0 1or

x ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (9)

the government can adopt compromised acceptance strategyto achieve partial stability -us five partial equilibriumpoints are formed

E1(0 0) E2(1 0) E3(0 1) E4(1 1)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(10)

-e Jacobi matrix replicated can be obtained by repli-cated dynamic equations (6) and (7)

J (1 minus 2x) yαR minus ΔRA minus βC + ΔL( 1113857 x(1 minus x)αR

y(1 minus y)(1 minus α)R (1 minus 2y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 11138591113890 1113891 (11)

It can get that the determinants det J and tr J of the Jacobimatrix are respectively

detJ (1 minus 2x)(1 minus 2y) yαR minus ΔRA minus βC + ΔL( 1113857 x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 minus xy(1 minus x)(1 minus y)αR(1 minus α)R

tr J (1 minus 2x) yαR minus ΔRA minus βC + ΔL( 1113857 +(1 minus 2y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859

(12)

Resident A

Government B

Rationalnegotiation A1

Violentresistance A2

Rational negotiationB1

Rational negotiationB1

Tough controlB2

Tough controlB2

RA + αR ndash βC RB + (1 ndash α)R ndash (1 ndash β)C RA ndash βC RB + ∆RB ndash ∆S RA + ∆RA ndash ∆L RB ndash (1 ndash β)C RA + ∆RA ndash ∆L RB + ∆RB ndash ∆S

Figure 1 Dynamic flow of evolutional game between the resident and the government in large-scale engineering projects

Complexity 5

It can get that the determinant and trace of the Jacobimatrix at five equilibrium points are shown in Table 2

Note T minus ΔRA + βC minus ΔL( 1113857 ΔRB +(1 minus β)C minus ΔS1113858 1113859 (1 minus α)R minus ΔRB +(1 minus β)C minus ΔS1113858 1113859 αR minus ΔRA + βC minus ΔL( 11138571113864 11138651113864 1113865

(1 minus α)RαR (13)

33 Multiscenario Evolutionary Game Analysis Afterobtaining the replication dynamic equation the next step isto analyze the evolutionary game equilibrium state of theresident and the government in the large-scale engineeringproject and its dynamic adjustment process under differentscenarios (the situation that the governmentrsquos extra stabilityexpenditures ΔS are different from the residentrsquos violentresistance cost ΔL)

331 Scenario One -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture and the residentrsquos violent resistance cost large then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

ΔLgt αRgtΔRA + βC(14)

Substituting above equations into the residentrsquo dynamicreplication equation (7) and the governmentrsquos replicationdynamic equation (8) it gets dxdtgt 0 dydtgt 0 In the 2 times

2 strategic space of the resident and the government theevolutionary phase map is shown in Figure 2(a) and theequilibrium result of the evolutionary game between theresident and the government is the only Nash equilibrium(rational negotiate A1 compromised acceptance B1)

When the governmentrsquos extra stability expenditure ΔSand the residentrsquos violent resistance cost ΔL are large boththe resident and the government will try to avoid adoptingstrategies that lead to deterioration of the situation (namelyviolent resistance and tough control) but will resolve con-flicts through rational negotiation in hope to gain the totalsocial revenue from the successful implementation of theproject

332 Scenario Two -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery small

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expenditure∆S and the residentrsquos violent resistance costΔL very small then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

αRgtΔRA + βCgtΔL(15)

For replication dynamic equation (6) of the resident if

ylowast

ΔRA + βC minus ΔL

αR (16)

then dxdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (17)

then dxdt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (18)

then dxdt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) of the government

if

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (19)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (20)

then dxdtgt 0 y⟶ 1 is the evolutionarily stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (21)

then dxdtlt 0 y⟶ 0 is the evolutionarily stable strategyIn the 2 times 2 strategic space between the government

and the resident by judging the positive and negativevalues of the determinant det J and the tr J of the fivepartial equilibrium points the points E1(0 0) and E4(1 1)

can be obtained as evolutionarily stable strategy thepoints E2(1 0) and E3(0 1) as unstable equilibriumpoints and the point

Table 1 -e payoff matrix of the evolutionary game between the resident and the government

Resident AGovernment B

Compromised acceptance B1 Tough control B2Rational negotiation A1 RA + αR minus βC RB + (1 minus α)R minus (1 minus β)C RA minus βC RB + ΔRB minus ΔSViolent resistance A2 RA + ΔRA minus ΔL RB minus (1 minus β)C RA + ΔRA minus ΔL RB + ΔRB minus ΔS

6 Complexity

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (22)

as unstable saddle points -e evolution phase diagram isshown in Figure 2(b)

When the governmentrsquos extra stability expenditure ∆Sand the residentrsquos violent resistance cost ΔL are very smallthe equilibrium result of the evolutionary game between theresident and the government in large-scale engineeringprojects is (rational negotiation A1 compromised accep-tance B1) or (violent resistanceA2 tough control B2) shownin Figure 2(b) -e specific evolutionary results are influ-enced by the initial state of social systems such as thestrength of the residentrsquos attitude to the large-scale engi-neering projects the expression manner of interest appeals

and the governmentrsquos ruling philosophy and the handlinghabits of the interest appeals When the initial state is locatedin region I and II in Figure 2(b) (namely quadrangleE1E2E5E3) evolution will converge to the point E1(0 0)then the resident adopts violent resistance strategy and thegovernment adopts tough control strategy When the initialstate is located in region III and IV in Figure 2(b) (namelyquadrangle E2E4E3E5) evolution will converge to the pointE4(1 1) then the resident adopts rational negotiationstrategy and the government adopts compromised accep-tance strategy

333 Scenario ree -e governmentrsquos extra stability ex-penditure ΔS is large and the residentrsquos violent resistancecost ΔL is small

Table 2 -e determinant and trace of the Jacobi matrix at five equilibrium points

Equilibriumpoint det J tr J

E1(00) (ΔRA + βC minus ΔL)[ΔRB + (1 minus β)C minus ΔS] minus (ΔRA + βC minus ΔL) minus [ΔR B + (1 minus β)C minus ΔS]

E2(10) (ΔRA + βC minus ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] (ΔRA + βC minus ΔL) + [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E3(01) (αR minus ΔRA minus βC + ΔL)[ΔRB + (1 minus β)C minus ΔS] (αR minus ΔRA minus βC + ΔL) + [ΔRB minus (1 minus β)C + ΔS]

E4(1 1) (αR minus ΔRA minus βC + ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] minus (αR minus ΔRA minus βC + ΔL) minus [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E5(xlowast ylowast) T 0

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

(a)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(b)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(c)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(d)

Figure 2 (a) -e equilibrium result when both ΔS and ΔL are large (b) the equilibrium result when both ΔS and ΔL are small (c) theequilibrium result when ΔS is large and ΔL is small (d) the equilibrium result when ΔS is small and ΔL is large

Complexity 7

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very large and the residentrsquos violent resistance cost∆L very small then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

αRgtΔRA + βCgtΔL(23)

For replication dynamic equation (6) when

ylowast

ΔRA + βC minus ΔL

αR (24)

then dtdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (25)

then dtdtgt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (26)

then dtdtlt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) nomatter what value xtakes dtdtgt 0 -erefore y⟶ 1 is the evolutionary stablestrategy

In the 2 times 2 strategic space between the government andthe resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the points E4(1 1) can be obtained asevolutionarily stable strategy points E1(0 0) E3(0 1) and

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (27)

as unstable saddle points and point E2(1 0) as unstablepoints -e evolution phase diagram is shown in Figure 2(c)

When the governmentrsquos extra stability expenditure ∆Sis large while the residentrsquos violent resistance cost ∆L issmall the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(c) Since thegovernmentrsquos extra stability expenditure is large thegovernment will try not to adopt tough control to increasespending but tend to adopt compromised acceptancestrategy At this time if the resident adopts violent resis-tance strategy they will increase their expenditure on theone hand (although the cost of violent resistance is small itis still greater than 0) and on the other hand asαRgtΔRA + βC αR minus βCgtΔRA is greater than 0 -e in-crease in revenue by adopting rational negotiation strategyis greater than that of the violent resistance strategy-erefore the resident will also tend to adopt the rationalnegotiation strategy

334 Scenario Four -e governmentrsquos extra stability ex-penditure ΔS is small and the residentrsquos violent resistancecost ΔL is large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very small and the residentrsquos violent resistance cost∆L very large then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

ΔLgt αRgtΔRA + βC(28)

For resident replication dynamic equation (6) no matterwhat value y takes dxdtgt 0 x⟶ 1 is the evolutionarystable strategy For government replication dynamic equa-tion (7) when

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (29)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (30)

then dxdtgt 0 y⟶ 1 is the evolutionary stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (31)

then dxdtlt 0 y⟶ 0 is the evolutionary stable strategyIn the 2 times 2 strategic space between the government and

the resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the point E4(1 1) is obtained as the evo-lutionary stable state points

E1(0 0) E2(1 0)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(32)

as unstable saddle points and point E3(0 1) as unstablepoints-e evolution phase diagram is shown in Figure 2(d)

When the governmentrsquos extra stability expenditure ∆Sis small and the residentrsquos violent resistance cost ∆L islarge the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(d) Since theresidentrsquos violent resistance cost is large the resident willtry not to adopt violent resistance to increase expenditurebut tend to adopt rational negotiation strategy At thistime if the government adopts tough control strategythey will increase their expenditure on the one hand(although the extra stability expenditure is small it is stillgreater than 0) and on the other hand as (1 minus α)RgtΔRB +

(1 minus β)C (1 minus α)RgtΔRB + (1 minus β)C is greater than 0 -eincrease in revenue by adopting compromised acceptancestrategy is greater than that of tough control strategy-erefore the government will also tend to adopt com-promised acceptance strategy

8 Complexity

4 Simulation Analysis of the Amplification ofStakeholder Conflict of Large-ScaleEngineering Projects on Complex Networks

41 Evolutionary Game Simulation Steps on ComplexNetworks Since Watts and Strogatz studied the averagepath length and clustering coefficient of the nematode neuralnetwork the American Western electrical power networkand the film actor cooperative network they found that ithad the characteristics of small world with average pathlength and large clustering coefficient and formally proposedthe small-world network [39] After long-term developmentthe small-world network has been proven to be effective inquantitatively studying the problems associated with com-plex social and economic systems -e network of multi-subject conflict amplification of large-scale engineeringprojects is essentially a complex network based on themultisubject interaction of realistic social networks andinfluenced by external systems such as social economicenvironment A large number of scholars studied the real-istic social network on the basis of complex networks andfound that its network topology had the characteristics ofsmall world with small average path length and largeclustering coefficient In view of the fact that the small-worldnetwork can help to explain problems related to complexsocial and economic systems and that the realistic com-munication network is similar to the small-world networkthe complex network structure type constructed in thispaper is a small-world network

For the simulation of the evolutionary game between theresident and the government in large-scale engineeringprojects on the complex network firstly we need to de-termine the strategic choice of individual players on thecomplex network then analyze the impact of differentnetwork characteristics on the evolutionary game resultsand explore the stakeholder conflict amplification mecha-nism of large-scale engineering projects

Firstly aWS small-world network with a certain numberof nodes is generated and network parameters are initial-ized All nodes on the network are divided into the twocategories of the resident and the government and theproportion of nodes on the network between the residentand the government is given -e meaning of the govern-ment includes all levels of governments government de-partments and officials related to the large-scale engineeringprojects -erefore the government is not only a node butshould also be regarded as multiple nodes on the networkand the number of which is much smaller than that of theresident nodes In the initial state the resident nodes ran-domly adopt the rational negotiation strategy A1 or theviolent resistance strategy A2 and the government noderandomly adopts the compromised acceptance strategy B1 orthe tough control strategy B2

Secondly in each round of the game each node on thecomplex network plays a game with all its neighbors and theresident and the government will change their own strategiesaccording to the updated rules after each round-e updatedrule is as follows the resident chooses to play games with its

neighbors if they are the same as the resident nodes thestrategy remains the same if they are government nodes andthe probability that the resident node changes the strategy is

pA 1

1 + exp UA1 minus UA2( 1113857ε1113858 11138591113864 1113865 (33)

-e probability that the government node changes thestrategy is

pB 1

1 + exp UB1 minus UB2( 1113857ε1113858 11138591113864 1113865 (34)

UA1 UA2 UB1 and UB2 can be respectively obtained byequations (1)ndash(4) ε denotes the noise coefficient whichindicates the interference of uncontrollable factors such asexternal impact on the node updating strategy-e larger theε is the larger the interference is Generally ε 05 is taken

Finally the above game process is repeated until the stateof each node on the network reaches a stable state -esimulation is terminated and the simulation result isobtained

42 Basic Variable Settings of NetLogo Simulation Platform-is paper uses the NetLogo simulation platform to carryout evolutionary game simulation research on the complexnetwork NetLogo is a multisubject programmable modelingenvironment that can be applied for natural and socialphenomena It can control thousands of individuals inmodeling and can simulate the behavior of microindividualsthe emergence of macroscopic modes and their relation-ships which is especially suitable for simulating complexsystems that evolve over time

According to the algorithm steps of the evolutionarygame simulation on the complex network firstly the WSsmall-world network is generated and all the nodes on thenetwork are divided into the two categories of the residentand the government In the initial NetLogo interface theinitial parameters of the network can be determined byadjusting the sliders of each parameter as shown in Figure 3

In Figure 3 the relevant initial parameters of the modelare on the left side For example ldquonum-nodesrdquo indicates thenetwork scale namely the total number of subjects on thenetwork ldquoRewiring-probabilityrdquo indicates the randomreconnection probability p of the WS small-world networkldquoGovernment-of-total-nodesrdquo indicates the proportion ofthe government subjects on the network to the total subjectsldquoInitial-xrdquo indicates the proportion that the resident choosesrational negotiation strategies in the initial state ldquoInitial-yrdquoindicates the proportion that the government choosescompromised acceptance in the initial state ldquoCitizen-ratio-of-income-increaserdquo indicates the proportion of the residentto the increased total revenue of the project for the societyand ldquocitizen-ratio-of-costrdquo indicates the proportion of thegovernment to the total cost of the project ldquoTotal-income-increaserdquo indicates the increased total revenue of the projectfor the society ldquoTotal-costrdquo indicates the cost that ensuresthe project going smoothly ldquoCitizen-extra-income-forcerdquoindicates the additional revenue from the residentrsquos violent

Complexity 9

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

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[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

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[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

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[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

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[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

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16 Complexity

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[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

but which is often opposed by the local people -is is calledthe ldquonot-in-my-backyardrdquo phenomenon [26]

Although China has a social economic and politicalbackground that is not completely consistent with Westernsociety the research on collective actions triggered by large-scale engineering projects in China is mainly focused onfactors that lead to collective action and the phenomenon ofldquoNot-In-My-Backyardrdquo Taking the Sanmenxia Dam Projectand the South-to-NorthWater Transfer Project in China as acase study Liu et al [27] use questionnaires semistructuredinterviews and structural equation models to study thecauses of collective action in Chinarsquos large constructionprojects By systematically summarizing the NIMBY phe-nomenon and combining with the background of Chinarsquoslarge-scale engineering projects Wang [28] believes that riskperception and risk amplification are the main causes ofsocial conflicts Liu et al [23] use Chinarsquos 2500 question-naires to study whether the NIMBY phenomenon is themain reason for the resident to oppose the construction ofurban infrastructure projects in China and conclude thatdepriving the residentrsquos participation rights is the mainreason for collective action In addition many Chinesescholars analyze the evolution process of resident incidentsbased on incidents triggered by large-scale engineeringprojects and propose corresponding prevention strategiesand governance strategies [29 30]

Conflicts are caused by imbalances in interests amongstakeholders and thus coordinating the relationship amongstakeholders is the key to resolving conflicts Game theory isoften used to study the relationship among engineeringproject stakeholders and resolve conflicts [31ndash33] Baroughet al [34] study the application of prisonerrsquos dilemma andchicken game in construction projects and consider thatstudying stakeholdersrsquo relations with game theory is veryhelpful for conflict management of engineering projectsKang et al [35] construct a three-stage game auction modelto analyze the relationship between the government and thebidding in the public-private partnership projects Based onthe game theory Wu et al [36] construct a decision modelfor the conflict behavior between the owner and the con-tractor compare the results under the two different con-ditions of nonconflict and conflict and study the influencesof conflict behavior of large-scale engineering projects onproject performance -ere are already many Chinesescholars who use the game theory to study the conflictsamong stakeholders of large-scale Chinese engineeringprojects [37ndash39] but most of which are studied under ahomogeneous social network structure However the con-nections among individuals in realistic life are not com-pletely random but have complex network characteristics ofsmall world and scale-free [40 41] Based on social relationssuch as interpersonal relationships stakeholders of large-scale engineering project form a complex interactive relationnetwork with characteristics of the complex network NowakandMay [42] study the prisonerrsquos dilemma game on the two-dimensional square and by combining the complex networktheory with the game theory he proposes the space gametheory thus the evolutionary game research on the complexnetwork begins to get a lot of concern [43 44] At present

the study of evolutionary games on complex networksmainly focuses on two aspects Firstly under the specificnetwork structure the effects of different evolution rules onthe evolution results are studied such as imitating the bestrule and imitating the winner rule Secondly there are al-ready many scholars who have been made on the influenceof different network structures on the game results such asrule network scale-free network and small-world networkand [45 46] In addition many scholars have carried outtargeted research in different fields such as finance andsociety Liu and Wang [47] constructed the coevolutionmodel of social network structure and strategy according tothe topology of social network and made a case study byusing the NetLogo social network simulation platformBased on the network association structure of investors Bianet al [48] established the simulation and evolution model ofherding behavior in the stock market under the strategy ofthe coordination game in the network and studied the keyfactors that influence the change of investment behavior ofstock market investors from the perspective of the networkBased on consumersrsquo different preferences for electric ve-hicles Fang et al [49] divided consumers into three types ofstakeholders to considering the time-varying demand ofelectric vehicle charging stations and gas stations andstudied the construction of electric vehicle charging infra-structure in the evolutionary game model of small-worldcomplex networks -erefore based on the identification ofthe major stakeholders of large-scale engineering projectsthis paper builds a game model about the evolution ofstakeholder conflicts amplification carries out simulationresearch on complex network to explore the impacts offactors such as complex network characteristics on the resultof evolutionary game

3 Evolutionary Game Model on StakeholderConflict Amplification in Large-ScaleEngineering Projects

31 Model Hypothesis Although there are many stake-holders in large-scale engineering projects including gov-ernments project developers contracts constructorsnearby residents relocated residents and general publiconly some of which play a key role in different problems Forthe social conflicts and social stability risks caused by en-gineering projects the stakeholders who play a key role areusually the core stakeholders such as the governmentproject developers and the resident [8 9 50] In Chinalarge-scale engineering projects are generally led by thegovernment while project developers undertake specifictasks such as project planning fund raising and con-struction implementation Especially for the handling ofsocial conflicts such as resident incidents it involves thebasic interests of the resident and the governmentrsquos emer-gency management capabilities which is mainly a gamebetween the government and the resident During thisprocess project developers mainly assist in relevant work ofthe government departments Most of Chinarsquos current large-scale engineering project conflict research studies group

Complexity 3

event evolution research studies and other related researchstudies are based on the game between the government andthe resident For example Liu et al take the urban demo-lition group events as the research object and take thegovernment and the resident as both sides of the game tostudy the conflict evolution of the urban demolition groupevents [29] Song and Liu [51] constructed a game modelbetween local governments and protesters and studied themechanism of resolving group events Based on existingresearch this paper considers the actual situation in Chinahighlighting the key stakeholders in the group events causedby large-scale engineering project conflicts On the otherhand this paper considers the complexity of the modelsimplifying the model so that the conflict evolution processand results can be shown more clearly -erefore this papermainly considers the government and the resident as bothsides of the evolutionary game -e basic hypothesis of theevolutionary game model of the stakeholder conflict am-plification is as follows

(1) In the evolutionary game model the two partici-pating groups are the resident (A) and the govern-ment (B)

(2) When related conflicts occur in large-scale engi-neering projects the resident has two strategies ofrational negotiation and violent resistance namelythe strategic space of the resident isSA rational negotiationA1 violent resistanceA21113864 1113865Moreover due to the differences of the local peoplein social and economic status and social relations theattitudes toward large-scale engineering projects arealso different-e resident take decentralized actionsin the strategic space rational negotiation1113864

A1 violent resistanceA2 Most people understandthe construction of large-scale engineering projectsand choose rational negotiation while some smallparts take excessive behavior for violent struggle-is hypothesis also conforms to participantsrsquo con-ventional behaviors in the evolutionary game and asmall part of the participants adopts hypothesis ofattempting behavior by the trial-and-error method

(3) Due to differences in governance concepts politicalachievements and support degree for large-scaleengineering projects there are two strategies ofcompromised acceptance and tough control in re-sponse to the reaction of the resident namely thestrategic space of the government which isSB compromise acceptanceB1 tough controlB21113864 1113865In this game the government will be affected byhigher-level governments and public opinions thusthe strategies adopted will be constantly adjusted

(4) According to the governmentrsquos relevant guaranteesand interest compensation the resident will makedecisions of rational negotiation or violent resis-tance which is in line with the ldquomyopiardquo hypothesison the decision of evolutionary games -e residentwill observe the benefits with corresponding deci-sions made by the people around them as a reference

for their own decisions Similarly when the gov-ernment responds to the reaction of the resident itwill also make strategic adjustments on the basis ofthe situations of the previous round

32 Dynamic Evolutionary Game Flow and Replication Dy-namic Equation -e specific game flow of the stakeholderconflict amplification and evolution in large-scale engi-neering projects is shown in Figure 1 which is mainly di-vided into two stages In the first stage when conflict issuesoccur the resident should either support the project andadopt rational negotiation strategy for their own relateddemands (namely A1) or they do not understand theproject or worry that the project construction will affect theecological environment and their own interests thusadopting violent resistance strategy for their own relateddemands (namely A2) When facing different strategies ofthe resident the government either chooses compromisedacceptance strategy (namely B1) or tough control strategy(namely B2)

Before the implementation of large-scale engineeringprojects the resident and the government have certainretained earnings which are respectively recorded as RA

and RB If both parties adopt moderate strategies (the res-ident adopts rational negotiation strategy and the govern-ment adopts compromised acceptance strategy) theincreased total revenue caused by the large-scale engineeringproject is R and the proportion of the resident is α(0lt αlt 1)-e total cost paid during the moderate negotiation processbetween the two parties is C and the share proportion of theresident is β(0lt βlt 1) Generally speaking large-scale en-gineering projects have a greater role in promoting localsocial and economic development so we believe that RgtCWhen the resident adopts rational negotiation strategy andthe government adopts tough control strategy neither partycan obtain the increased revenue from the large-scale en-gineering projects Due to the attempt to adopt negotiationstrategy the resident will still need to pay the correspondingcost under mild negotiation Because the government adoptstough control strategy and does not need to bear the costunder a moderate negotiation state it needs to increase themaintenance expenditure ΔS for the tough control In theprocess it also gets the additional income ΔRB from theproject When the resident chooses the violent resistancestrategy and the government chooses compromised accep-tance strategies the resident needs to bear the cost of violentresistance ΔL but they will also receive additional com-pensation ΔRA from the project At this time as the gov-ernment tries to adopt the compromised acceptancestrategy and it needs to pay the corresponding cost underthe mild negotiation When the resident chooses violentresistance strategy and the government chooses the toughcontrol strategy both parties should undertake extra cost ofviolent resistance and maintenance expenditure for theirstrong attitude but at the same time they can also getadditional income and interest compensation from theproject -e payoff matrix of the evolutionary game between

4 Complexity

the resident and the government of the large-scale engi-neering projects is shown in Table 1

Assuming that the proportion of rational negotiationstrategy A1 adopted by the resident is x and that of com-promised acceptance strategy B1 adopted by the governmentis y the expected revenue of rational negotiation strategy A1and violent resistance strategy A2 adopted by resident arerespectively

UA1 yαR + RA minus βC (1)

UA2 RA + ΔRA minus ΔL (2)

-e expected revenue of the compromised acceptancestrategy B1 and tough control strategy B2 that the gov-ernment adopts are respectively

UB1 x(1 minus α)R + RB minus (1 minus β)C (3)

UB2 RB + ΔRB minus ΔS (4)

It can get that the expected revenue of the resident andthe government is respectivelyUA x yαR minus ΔRA minus βC + ΔL( 1113857 + RA + ΔRA minus ΔL

UB y x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 + RB + ΔRB minus ΔS

(5)

It can further get that the replicated dynamic equationsof the resident and government are respectively

dx

dt x(1 minus x) yαR minus ΔRA minus βC + ΔL( 1113857 (6)

dx

dt y(1 minus y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 (7)

In can be known from formula (6) that when x 0 1 or

y ΔRA + βC minus ΔL

αR (8)

the resident can achieve partial stability by adopting therational negotiation strategy from formula (7) when y 0 1or

x ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (9)

the government can adopt compromised acceptance strategyto achieve partial stability -us five partial equilibriumpoints are formed

E1(0 0) E2(1 0) E3(0 1) E4(1 1)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(10)

-e Jacobi matrix replicated can be obtained by repli-cated dynamic equations (6) and (7)

J (1 minus 2x) yαR minus ΔRA minus βC + ΔL( 1113857 x(1 minus x)αR

y(1 minus y)(1 minus α)R (1 minus 2y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 11138591113890 1113891 (11)

It can get that the determinants det J and tr J of the Jacobimatrix are respectively

detJ (1 minus 2x)(1 minus 2y) yαR minus ΔRA minus βC + ΔL( 1113857 x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 minus xy(1 minus x)(1 minus y)αR(1 minus α)R

tr J (1 minus 2x) yαR minus ΔRA minus βC + ΔL( 1113857 +(1 minus 2y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859

(12)

Resident A

Government B

Rationalnegotiation A1

Violentresistance A2

Rational negotiationB1

Rational negotiationB1

Tough controlB2

Tough controlB2

RA + αR ndash βC RB + (1 ndash α)R ndash (1 ndash β)C RA ndash βC RB + ∆RB ndash ∆S RA + ∆RA ndash ∆L RB ndash (1 ndash β)C RA + ∆RA ndash ∆L RB + ∆RB ndash ∆S

Figure 1 Dynamic flow of evolutional game between the resident and the government in large-scale engineering projects

Complexity 5

It can get that the determinant and trace of the Jacobimatrix at five equilibrium points are shown in Table 2

Note T minus ΔRA + βC minus ΔL( 1113857 ΔRB +(1 minus β)C minus ΔS1113858 1113859 (1 minus α)R minus ΔRB +(1 minus β)C minus ΔS1113858 1113859 αR minus ΔRA + βC minus ΔL( 11138571113864 11138651113864 1113865

(1 minus α)RαR (13)

33 Multiscenario Evolutionary Game Analysis Afterobtaining the replication dynamic equation the next step isto analyze the evolutionary game equilibrium state of theresident and the government in the large-scale engineeringproject and its dynamic adjustment process under differentscenarios (the situation that the governmentrsquos extra stabilityexpenditures ΔS are different from the residentrsquos violentresistance cost ΔL)

331 Scenario One -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture and the residentrsquos violent resistance cost large then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

ΔLgt αRgtΔRA + βC(14)

Substituting above equations into the residentrsquo dynamicreplication equation (7) and the governmentrsquos replicationdynamic equation (8) it gets dxdtgt 0 dydtgt 0 In the 2 times

2 strategic space of the resident and the government theevolutionary phase map is shown in Figure 2(a) and theequilibrium result of the evolutionary game between theresident and the government is the only Nash equilibrium(rational negotiate A1 compromised acceptance B1)

When the governmentrsquos extra stability expenditure ΔSand the residentrsquos violent resistance cost ΔL are large boththe resident and the government will try to avoid adoptingstrategies that lead to deterioration of the situation (namelyviolent resistance and tough control) but will resolve con-flicts through rational negotiation in hope to gain the totalsocial revenue from the successful implementation of theproject

332 Scenario Two -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery small

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expenditure∆S and the residentrsquos violent resistance costΔL very small then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

αRgtΔRA + βCgtΔL(15)

For replication dynamic equation (6) of the resident if

ylowast

ΔRA + βC minus ΔL

αR (16)

then dxdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (17)

then dxdt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (18)

then dxdt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) of the government

if

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (19)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (20)

then dxdtgt 0 y⟶ 1 is the evolutionarily stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (21)

then dxdtlt 0 y⟶ 0 is the evolutionarily stable strategyIn the 2 times 2 strategic space between the government

and the resident by judging the positive and negativevalues of the determinant det J and the tr J of the fivepartial equilibrium points the points E1(0 0) and E4(1 1)

can be obtained as evolutionarily stable strategy thepoints E2(1 0) and E3(0 1) as unstable equilibriumpoints and the point

Table 1 -e payoff matrix of the evolutionary game between the resident and the government

Resident AGovernment B

Compromised acceptance B1 Tough control B2Rational negotiation A1 RA + αR minus βC RB + (1 minus α)R minus (1 minus β)C RA minus βC RB + ΔRB minus ΔSViolent resistance A2 RA + ΔRA minus ΔL RB minus (1 minus β)C RA + ΔRA minus ΔL RB + ΔRB minus ΔS

6 Complexity

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (22)

as unstable saddle points -e evolution phase diagram isshown in Figure 2(b)

When the governmentrsquos extra stability expenditure ∆Sand the residentrsquos violent resistance cost ΔL are very smallthe equilibrium result of the evolutionary game between theresident and the government in large-scale engineeringprojects is (rational negotiation A1 compromised accep-tance B1) or (violent resistanceA2 tough control B2) shownin Figure 2(b) -e specific evolutionary results are influ-enced by the initial state of social systems such as thestrength of the residentrsquos attitude to the large-scale engi-neering projects the expression manner of interest appeals

and the governmentrsquos ruling philosophy and the handlinghabits of the interest appeals When the initial state is locatedin region I and II in Figure 2(b) (namely quadrangleE1E2E5E3) evolution will converge to the point E1(0 0)then the resident adopts violent resistance strategy and thegovernment adopts tough control strategy When the initialstate is located in region III and IV in Figure 2(b) (namelyquadrangle E2E4E3E5) evolution will converge to the pointE4(1 1) then the resident adopts rational negotiationstrategy and the government adopts compromised accep-tance strategy

333 Scenario ree -e governmentrsquos extra stability ex-penditure ΔS is large and the residentrsquos violent resistancecost ΔL is small

Table 2 -e determinant and trace of the Jacobi matrix at five equilibrium points

Equilibriumpoint det J tr J

E1(00) (ΔRA + βC minus ΔL)[ΔRB + (1 minus β)C minus ΔS] minus (ΔRA + βC minus ΔL) minus [ΔR B + (1 minus β)C minus ΔS]

E2(10) (ΔRA + βC minus ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] (ΔRA + βC minus ΔL) + [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E3(01) (αR minus ΔRA minus βC + ΔL)[ΔRB + (1 minus β)C minus ΔS] (αR minus ΔRA minus βC + ΔL) + [ΔRB minus (1 minus β)C + ΔS]

E4(1 1) (αR minus ΔRA minus βC + ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] minus (αR minus ΔRA minus βC + ΔL) minus [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E5(xlowast ylowast) T 0

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

(a)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(b)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(c)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(d)

Figure 2 (a) -e equilibrium result when both ΔS and ΔL are large (b) the equilibrium result when both ΔS and ΔL are small (c) theequilibrium result when ΔS is large and ΔL is small (d) the equilibrium result when ΔS is small and ΔL is large

Complexity 7

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very large and the residentrsquos violent resistance cost∆L very small then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

αRgtΔRA + βCgtΔL(23)

For replication dynamic equation (6) when

ylowast

ΔRA + βC minus ΔL

αR (24)

then dtdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (25)

then dtdtgt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (26)

then dtdtlt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) nomatter what value xtakes dtdtgt 0 -erefore y⟶ 1 is the evolutionary stablestrategy

In the 2 times 2 strategic space between the government andthe resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the points E4(1 1) can be obtained asevolutionarily stable strategy points E1(0 0) E3(0 1) and

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (27)

as unstable saddle points and point E2(1 0) as unstablepoints -e evolution phase diagram is shown in Figure 2(c)

When the governmentrsquos extra stability expenditure ∆Sis large while the residentrsquos violent resistance cost ∆L issmall the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(c) Since thegovernmentrsquos extra stability expenditure is large thegovernment will try not to adopt tough control to increasespending but tend to adopt compromised acceptancestrategy At this time if the resident adopts violent resis-tance strategy they will increase their expenditure on theone hand (although the cost of violent resistance is small itis still greater than 0) and on the other hand asαRgtΔRA + βC αR minus βCgtΔRA is greater than 0 -e in-crease in revenue by adopting rational negotiation strategyis greater than that of the violent resistance strategy-erefore the resident will also tend to adopt the rationalnegotiation strategy

334 Scenario Four -e governmentrsquos extra stability ex-penditure ΔS is small and the residentrsquos violent resistancecost ΔL is large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very small and the residentrsquos violent resistance cost∆L very large then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

ΔLgt αRgtΔRA + βC(28)

For resident replication dynamic equation (6) no matterwhat value y takes dxdtgt 0 x⟶ 1 is the evolutionarystable strategy For government replication dynamic equa-tion (7) when

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (29)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (30)

then dxdtgt 0 y⟶ 1 is the evolutionary stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (31)

then dxdtlt 0 y⟶ 0 is the evolutionary stable strategyIn the 2 times 2 strategic space between the government and

the resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the point E4(1 1) is obtained as the evo-lutionary stable state points

E1(0 0) E2(1 0)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(32)

as unstable saddle points and point E3(0 1) as unstablepoints-e evolution phase diagram is shown in Figure 2(d)

When the governmentrsquos extra stability expenditure ∆Sis small and the residentrsquos violent resistance cost ∆L islarge the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(d) Since theresidentrsquos violent resistance cost is large the resident willtry not to adopt violent resistance to increase expenditurebut tend to adopt rational negotiation strategy At thistime if the government adopts tough control strategythey will increase their expenditure on the one hand(although the extra stability expenditure is small it is stillgreater than 0) and on the other hand as (1 minus α)RgtΔRB +

(1 minus β)C (1 minus α)RgtΔRB + (1 minus β)C is greater than 0 -eincrease in revenue by adopting compromised acceptancestrategy is greater than that of tough control strategy-erefore the government will also tend to adopt com-promised acceptance strategy

8 Complexity

4 Simulation Analysis of the Amplification ofStakeholder Conflict of Large-ScaleEngineering Projects on Complex Networks

41 Evolutionary Game Simulation Steps on ComplexNetworks Since Watts and Strogatz studied the averagepath length and clustering coefficient of the nematode neuralnetwork the American Western electrical power networkand the film actor cooperative network they found that ithad the characteristics of small world with average pathlength and large clustering coefficient and formally proposedthe small-world network [39] After long-term developmentthe small-world network has been proven to be effective inquantitatively studying the problems associated with com-plex social and economic systems -e network of multi-subject conflict amplification of large-scale engineeringprojects is essentially a complex network based on themultisubject interaction of realistic social networks andinfluenced by external systems such as social economicenvironment A large number of scholars studied the real-istic social network on the basis of complex networks andfound that its network topology had the characteristics ofsmall world with small average path length and largeclustering coefficient In view of the fact that the small-worldnetwork can help to explain problems related to complexsocial and economic systems and that the realistic com-munication network is similar to the small-world networkthe complex network structure type constructed in thispaper is a small-world network

For the simulation of the evolutionary game between theresident and the government in large-scale engineeringprojects on the complex network firstly we need to de-termine the strategic choice of individual players on thecomplex network then analyze the impact of differentnetwork characteristics on the evolutionary game resultsand explore the stakeholder conflict amplification mecha-nism of large-scale engineering projects

Firstly aWS small-world network with a certain numberof nodes is generated and network parameters are initial-ized All nodes on the network are divided into the twocategories of the resident and the government and theproportion of nodes on the network between the residentand the government is given -e meaning of the govern-ment includes all levels of governments government de-partments and officials related to the large-scale engineeringprojects -erefore the government is not only a node butshould also be regarded as multiple nodes on the networkand the number of which is much smaller than that of theresident nodes In the initial state the resident nodes ran-domly adopt the rational negotiation strategy A1 or theviolent resistance strategy A2 and the government noderandomly adopts the compromised acceptance strategy B1 orthe tough control strategy B2

Secondly in each round of the game each node on thecomplex network plays a game with all its neighbors and theresident and the government will change their own strategiesaccording to the updated rules after each round-e updatedrule is as follows the resident chooses to play games with its

neighbors if they are the same as the resident nodes thestrategy remains the same if they are government nodes andthe probability that the resident node changes the strategy is

pA 1

1 + exp UA1 minus UA2( 1113857ε1113858 11138591113864 1113865 (33)

-e probability that the government node changes thestrategy is

pB 1

1 + exp UB1 minus UB2( 1113857ε1113858 11138591113864 1113865 (34)

UA1 UA2 UB1 and UB2 can be respectively obtained byequations (1)ndash(4) ε denotes the noise coefficient whichindicates the interference of uncontrollable factors such asexternal impact on the node updating strategy-e larger theε is the larger the interference is Generally ε 05 is taken

Finally the above game process is repeated until the stateof each node on the network reaches a stable state -esimulation is terminated and the simulation result isobtained

42 Basic Variable Settings of NetLogo Simulation Platform-is paper uses the NetLogo simulation platform to carryout evolutionary game simulation research on the complexnetwork NetLogo is a multisubject programmable modelingenvironment that can be applied for natural and socialphenomena It can control thousands of individuals inmodeling and can simulate the behavior of microindividualsthe emergence of macroscopic modes and their relation-ships which is especially suitable for simulating complexsystems that evolve over time

According to the algorithm steps of the evolutionarygame simulation on the complex network firstly the WSsmall-world network is generated and all the nodes on thenetwork are divided into the two categories of the residentand the government In the initial NetLogo interface theinitial parameters of the network can be determined byadjusting the sliders of each parameter as shown in Figure 3

In Figure 3 the relevant initial parameters of the modelare on the left side For example ldquonum-nodesrdquo indicates thenetwork scale namely the total number of subjects on thenetwork ldquoRewiring-probabilityrdquo indicates the randomreconnection probability p of the WS small-world networkldquoGovernment-of-total-nodesrdquo indicates the proportion ofthe government subjects on the network to the total subjectsldquoInitial-xrdquo indicates the proportion that the resident choosesrational negotiation strategies in the initial state ldquoInitial-yrdquoindicates the proportion that the government choosescompromised acceptance in the initial state ldquoCitizen-ratio-of-income-increaserdquo indicates the proportion of the residentto the increased total revenue of the project for the societyand ldquocitizen-ratio-of-costrdquo indicates the proportion of thegovernment to the total cost of the project ldquoTotal-income-increaserdquo indicates the increased total revenue of the projectfor the society ldquoTotal-costrdquo indicates the cost that ensuresthe project going smoothly ldquoCitizen-extra-income-forcerdquoindicates the additional revenue from the residentrsquos violent

Complexity 9

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

event evolution research studies and other related researchstudies are based on the game between the government andthe resident For example Liu et al take the urban demo-lition group events as the research object and take thegovernment and the resident as both sides of the game tostudy the conflict evolution of the urban demolition groupevents [29] Song and Liu [51] constructed a game modelbetween local governments and protesters and studied themechanism of resolving group events Based on existingresearch this paper considers the actual situation in Chinahighlighting the key stakeholders in the group events causedby large-scale engineering project conflicts On the otherhand this paper considers the complexity of the modelsimplifying the model so that the conflict evolution processand results can be shown more clearly -erefore this papermainly considers the government and the resident as bothsides of the evolutionary game -e basic hypothesis of theevolutionary game model of the stakeholder conflict am-plification is as follows

(1) In the evolutionary game model the two partici-pating groups are the resident (A) and the govern-ment (B)

(2) When related conflicts occur in large-scale engi-neering projects the resident has two strategies ofrational negotiation and violent resistance namelythe strategic space of the resident isSA rational negotiationA1 violent resistanceA21113864 1113865Moreover due to the differences of the local peoplein social and economic status and social relations theattitudes toward large-scale engineering projects arealso different-e resident take decentralized actionsin the strategic space rational negotiation1113864

A1 violent resistanceA2 Most people understandthe construction of large-scale engineering projectsand choose rational negotiation while some smallparts take excessive behavior for violent struggle-is hypothesis also conforms to participantsrsquo con-ventional behaviors in the evolutionary game and asmall part of the participants adopts hypothesis ofattempting behavior by the trial-and-error method

(3) Due to differences in governance concepts politicalachievements and support degree for large-scaleengineering projects there are two strategies ofcompromised acceptance and tough control in re-sponse to the reaction of the resident namely thestrategic space of the government which isSB compromise acceptanceB1 tough controlB21113864 1113865In this game the government will be affected byhigher-level governments and public opinions thusthe strategies adopted will be constantly adjusted

(4) According to the governmentrsquos relevant guaranteesand interest compensation the resident will makedecisions of rational negotiation or violent resis-tance which is in line with the ldquomyopiardquo hypothesison the decision of evolutionary games -e residentwill observe the benefits with corresponding deci-sions made by the people around them as a reference

for their own decisions Similarly when the gov-ernment responds to the reaction of the resident itwill also make strategic adjustments on the basis ofthe situations of the previous round

32 Dynamic Evolutionary Game Flow and Replication Dy-namic Equation -e specific game flow of the stakeholderconflict amplification and evolution in large-scale engi-neering projects is shown in Figure 1 which is mainly di-vided into two stages In the first stage when conflict issuesoccur the resident should either support the project andadopt rational negotiation strategy for their own relateddemands (namely A1) or they do not understand theproject or worry that the project construction will affect theecological environment and their own interests thusadopting violent resistance strategy for their own relateddemands (namely A2) When facing different strategies ofthe resident the government either chooses compromisedacceptance strategy (namely B1) or tough control strategy(namely B2)

Before the implementation of large-scale engineeringprojects the resident and the government have certainretained earnings which are respectively recorded as RA

and RB If both parties adopt moderate strategies (the res-ident adopts rational negotiation strategy and the govern-ment adopts compromised acceptance strategy) theincreased total revenue caused by the large-scale engineeringproject is R and the proportion of the resident is α(0lt αlt 1)-e total cost paid during the moderate negotiation processbetween the two parties is C and the share proportion of theresident is β(0lt βlt 1) Generally speaking large-scale en-gineering projects have a greater role in promoting localsocial and economic development so we believe that RgtCWhen the resident adopts rational negotiation strategy andthe government adopts tough control strategy neither partycan obtain the increased revenue from the large-scale en-gineering projects Due to the attempt to adopt negotiationstrategy the resident will still need to pay the correspondingcost under mild negotiation Because the government adoptstough control strategy and does not need to bear the costunder a moderate negotiation state it needs to increase themaintenance expenditure ΔS for the tough control In theprocess it also gets the additional income ΔRB from theproject When the resident chooses the violent resistancestrategy and the government chooses compromised accep-tance strategies the resident needs to bear the cost of violentresistance ΔL but they will also receive additional com-pensation ΔRA from the project At this time as the gov-ernment tries to adopt the compromised acceptancestrategy and it needs to pay the corresponding cost underthe mild negotiation When the resident chooses violentresistance strategy and the government chooses the toughcontrol strategy both parties should undertake extra cost ofviolent resistance and maintenance expenditure for theirstrong attitude but at the same time they can also getadditional income and interest compensation from theproject -e payoff matrix of the evolutionary game between

4 Complexity

the resident and the government of the large-scale engi-neering projects is shown in Table 1

Assuming that the proportion of rational negotiationstrategy A1 adopted by the resident is x and that of com-promised acceptance strategy B1 adopted by the governmentis y the expected revenue of rational negotiation strategy A1and violent resistance strategy A2 adopted by resident arerespectively

UA1 yαR + RA minus βC (1)

UA2 RA + ΔRA minus ΔL (2)

-e expected revenue of the compromised acceptancestrategy B1 and tough control strategy B2 that the gov-ernment adopts are respectively

UB1 x(1 minus α)R + RB minus (1 minus β)C (3)

UB2 RB + ΔRB minus ΔS (4)

It can get that the expected revenue of the resident andthe government is respectivelyUA x yαR minus ΔRA minus βC + ΔL( 1113857 + RA + ΔRA minus ΔL

UB y x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 + RB + ΔRB minus ΔS

(5)

It can further get that the replicated dynamic equationsof the resident and government are respectively

dx

dt x(1 minus x) yαR minus ΔRA minus βC + ΔL( 1113857 (6)

dx

dt y(1 minus y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 (7)

In can be known from formula (6) that when x 0 1 or

y ΔRA + βC minus ΔL

αR (8)

the resident can achieve partial stability by adopting therational negotiation strategy from formula (7) when y 0 1or

x ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (9)

the government can adopt compromised acceptance strategyto achieve partial stability -us five partial equilibriumpoints are formed

E1(0 0) E2(1 0) E3(0 1) E4(1 1)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(10)

-e Jacobi matrix replicated can be obtained by repli-cated dynamic equations (6) and (7)

J (1 minus 2x) yαR minus ΔRA minus βC + ΔL( 1113857 x(1 minus x)αR

y(1 minus y)(1 minus α)R (1 minus 2y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 11138591113890 1113891 (11)

It can get that the determinants det J and tr J of the Jacobimatrix are respectively

detJ (1 minus 2x)(1 minus 2y) yαR minus ΔRA minus βC + ΔL( 1113857 x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 minus xy(1 minus x)(1 minus y)αR(1 minus α)R

tr J (1 minus 2x) yαR minus ΔRA minus βC + ΔL( 1113857 +(1 minus 2y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859

(12)

Resident A

Government B

Rationalnegotiation A1

Violentresistance A2

Rational negotiationB1

Rational negotiationB1

Tough controlB2

Tough controlB2

RA + αR ndash βC RB + (1 ndash α)R ndash (1 ndash β)C RA ndash βC RB + ∆RB ndash ∆S RA + ∆RA ndash ∆L RB ndash (1 ndash β)C RA + ∆RA ndash ∆L RB + ∆RB ndash ∆S

Figure 1 Dynamic flow of evolutional game between the resident and the government in large-scale engineering projects

Complexity 5

It can get that the determinant and trace of the Jacobimatrix at five equilibrium points are shown in Table 2

Note T minus ΔRA + βC minus ΔL( 1113857 ΔRB +(1 minus β)C minus ΔS1113858 1113859 (1 minus α)R minus ΔRB +(1 minus β)C minus ΔS1113858 1113859 αR minus ΔRA + βC minus ΔL( 11138571113864 11138651113864 1113865

(1 minus α)RαR (13)

33 Multiscenario Evolutionary Game Analysis Afterobtaining the replication dynamic equation the next step isto analyze the evolutionary game equilibrium state of theresident and the government in the large-scale engineeringproject and its dynamic adjustment process under differentscenarios (the situation that the governmentrsquos extra stabilityexpenditures ΔS are different from the residentrsquos violentresistance cost ΔL)

331 Scenario One -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture and the residentrsquos violent resistance cost large then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

ΔLgt αRgtΔRA + βC(14)

Substituting above equations into the residentrsquo dynamicreplication equation (7) and the governmentrsquos replicationdynamic equation (8) it gets dxdtgt 0 dydtgt 0 In the 2 times

2 strategic space of the resident and the government theevolutionary phase map is shown in Figure 2(a) and theequilibrium result of the evolutionary game between theresident and the government is the only Nash equilibrium(rational negotiate A1 compromised acceptance B1)

When the governmentrsquos extra stability expenditure ΔSand the residentrsquos violent resistance cost ΔL are large boththe resident and the government will try to avoid adoptingstrategies that lead to deterioration of the situation (namelyviolent resistance and tough control) but will resolve con-flicts through rational negotiation in hope to gain the totalsocial revenue from the successful implementation of theproject

332 Scenario Two -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery small

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expenditure∆S and the residentrsquos violent resistance costΔL very small then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

αRgtΔRA + βCgtΔL(15)

For replication dynamic equation (6) of the resident if

ylowast

ΔRA + βC minus ΔL

αR (16)

then dxdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (17)

then dxdt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (18)

then dxdt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) of the government

if

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (19)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (20)

then dxdtgt 0 y⟶ 1 is the evolutionarily stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (21)

then dxdtlt 0 y⟶ 0 is the evolutionarily stable strategyIn the 2 times 2 strategic space between the government

and the resident by judging the positive and negativevalues of the determinant det J and the tr J of the fivepartial equilibrium points the points E1(0 0) and E4(1 1)

can be obtained as evolutionarily stable strategy thepoints E2(1 0) and E3(0 1) as unstable equilibriumpoints and the point

Table 1 -e payoff matrix of the evolutionary game between the resident and the government

Resident AGovernment B

Compromised acceptance B1 Tough control B2Rational negotiation A1 RA + αR minus βC RB + (1 minus α)R minus (1 minus β)C RA minus βC RB + ΔRB minus ΔSViolent resistance A2 RA + ΔRA minus ΔL RB minus (1 minus β)C RA + ΔRA minus ΔL RB + ΔRB minus ΔS

6 Complexity

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (22)

as unstable saddle points -e evolution phase diagram isshown in Figure 2(b)

When the governmentrsquos extra stability expenditure ∆Sand the residentrsquos violent resistance cost ΔL are very smallthe equilibrium result of the evolutionary game between theresident and the government in large-scale engineeringprojects is (rational negotiation A1 compromised accep-tance B1) or (violent resistanceA2 tough control B2) shownin Figure 2(b) -e specific evolutionary results are influ-enced by the initial state of social systems such as thestrength of the residentrsquos attitude to the large-scale engi-neering projects the expression manner of interest appeals

and the governmentrsquos ruling philosophy and the handlinghabits of the interest appeals When the initial state is locatedin region I and II in Figure 2(b) (namely quadrangleE1E2E5E3) evolution will converge to the point E1(0 0)then the resident adopts violent resistance strategy and thegovernment adopts tough control strategy When the initialstate is located in region III and IV in Figure 2(b) (namelyquadrangle E2E4E3E5) evolution will converge to the pointE4(1 1) then the resident adopts rational negotiationstrategy and the government adopts compromised accep-tance strategy

333 Scenario ree -e governmentrsquos extra stability ex-penditure ΔS is large and the residentrsquos violent resistancecost ΔL is small

Table 2 -e determinant and trace of the Jacobi matrix at five equilibrium points

Equilibriumpoint det J tr J

E1(00) (ΔRA + βC minus ΔL)[ΔRB + (1 minus β)C minus ΔS] minus (ΔRA + βC minus ΔL) minus [ΔR B + (1 minus β)C minus ΔS]

E2(10) (ΔRA + βC minus ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] (ΔRA + βC minus ΔL) + [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E3(01) (αR minus ΔRA minus βC + ΔL)[ΔRB + (1 minus β)C minus ΔS] (αR minus ΔRA minus βC + ΔL) + [ΔRB minus (1 minus β)C + ΔS]

E4(1 1) (αR minus ΔRA minus βC + ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] minus (αR minus ΔRA minus βC + ΔL) minus [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E5(xlowast ylowast) T 0

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

(a)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(b)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(c)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(d)

Figure 2 (a) -e equilibrium result when both ΔS and ΔL are large (b) the equilibrium result when both ΔS and ΔL are small (c) theequilibrium result when ΔS is large and ΔL is small (d) the equilibrium result when ΔS is small and ΔL is large

Complexity 7

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very large and the residentrsquos violent resistance cost∆L very small then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

αRgtΔRA + βCgtΔL(23)

For replication dynamic equation (6) when

ylowast

ΔRA + βC minus ΔL

αR (24)

then dtdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (25)

then dtdtgt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (26)

then dtdtlt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) nomatter what value xtakes dtdtgt 0 -erefore y⟶ 1 is the evolutionary stablestrategy

In the 2 times 2 strategic space between the government andthe resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the points E4(1 1) can be obtained asevolutionarily stable strategy points E1(0 0) E3(0 1) and

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (27)

as unstable saddle points and point E2(1 0) as unstablepoints -e evolution phase diagram is shown in Figure 2(c)

When the governmentrsquos extra stability expenditure ∆Sis large while the residentrsquos violent resistance cost ∆L issmall the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(c) Since thegovernmentrsquos extra stability expenditure is large thegovernment will try not to adopt tough control to increasespending but tend to adopt compromised acceptancestrategy At this time if the resident adopts violent resis-tance strategy they will increase their expenditure on theone hand (although the cost of violent resistance is small itis still greater than 0) and on the other hand asαRgtΔRA + βC αR minus βCgtΔRA is greater than 0 -e in-crease in revenue by adopting rational negotiation strategyis greater than that of the violent resistance strategy-erefore the resident will also tend to adopt the rationalnegotiation strategy

334 Scenario Four -e governmentrsquos extra stability ex-penditure ΔS is small and the residentrsquos violent resistancecost ΔL is large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very small and the residentrsquos violent resistance cost∆L very large then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

ΔLgt αRgtΔRA + βC(28)

For resident replication dynamic equation (6) no matterwhat value y takes dxdtgt 0 x⟶ 1 is the evolutionarystable strategy For government replication dynamic equa-tion (7) when

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (29)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (30)

then dxdtgt 0 y⟶ 1 is the evolutionary stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (31)

then dxdtlt 0 y⟶ 0 is the evolutionary stable strategyIn the 2 times 2 strategic space between the government and

the resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the point E4(1 1) is obtained as the evo-lutionary stable state points

E1(0 0) E2(1 0)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(32)

as unstable saddle points and point E3(0 1) as unstablepoints-e evolution phase diagram is shown in Figure 2(d)

When the governmentrsquos extra stability expenditure ∆Sis small and the residentrsquos violent resistance cost ∆L islarge the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(d) Since theresidentrsquos violent resistance cost is large the resident willtry not to adopt violent resistance to increase expenditurebut tend to adopt rational negotiation strategy At thistime if the government adopts tough control strategythey will increase their expenditure on the one hand(although the extra stability expenditure is small it is stillgreater than 0) and on the other hand as (1 minus α)RgtΔRB +

(1 minus β)C (1 minus α)RgtΔRB + (1 minus β)C is greater than 0 -eincrease in revenue by adopting compromised acceptancestrategy is greater than that of tough control strategy-erefore the government will also tend to adopt com-promised acceptance strategy

8 Complexity

4 Simulation Analysis of the Amplification ofStakeholder Conflict of Large-ScaleEngineering Projects on Complex Networks

41 Evolutionary Game Simulation Steps on ComplexNetworks Since Watts and Strogatz studied the averagepath length and clustering coefficient of the nematode neuralnetwork the American Western electrical power networkand the film actor cooperative network they found that ithad the characteristics of small world with average pathlength and large clustering coefficient and formally proposedthe small-world network [39] After long-term developmentthe small-world network has been proven to be effective inquantitatively studying the problems associated with com-plex social and economic systems -e network of multi-subject conflict amplification of large-scale engineeringprojects is essentially a complex network based on themultisubject interaction of realistic social networks andinfluenced by external systems such as social economicenvironment A large number of scholars studied the real-istic social network on the basis of complex networks andfound that its network topology had the characteristics ofsmall world with small average path length and largeclustering coefficient In view of the fact that the small-worldnetwork can help to explain problems related to complexsocial and economic systems and that the realistic com-munication network is similar to the small-world networkthe complex network structure type constructed in thispaper is a small-world network

For the simulation of the evolutionary game between theresident and the government in large-scale engineeringprojects on the complex network firstly we need to de-termine the strategic choice of individual players on thecomplex network then analyze the impact of differentnetwork characteristics on the evolutionary game resultsand explore the stakeholder conflict amplification mecha-nism of large-scale engineering projects

Firstly aWS small-world network with a certain numberof nodes is generated and network parameters are initial-ized All nodes on the network are divided into the twocategories of the resident and the government and theproportion of nodes on the network between the residentand the government is given -e meaning of the govern-ment includes all levels of governments government de-partments and officials related to the large-scale engineeringprojects -erefore the government is not only a node butshould also be regarded as multiple nodes on the networkand the number of which is much smaller than that of theresident nodes In the initial state the resident nodes ran-domly adopt the rational negotiation strategy A1 or theviolent resistance strategy A2 and the government noderandomly adopts the compromised acceptance strategy B1 orthe tough control strategy B2

Secondly in each round of the game each node on thecomplex network plays a game with all its neighbors and theresident and the government will change their own strategiesaccording to the updated rules after each round-e updatedrule is as follows the resident chooses to play games with its

neighbors if they are the same as the resident nodes thestrategy remains the same if they are government nodes andthe probability that the resident node changes the strategy is

pA 1

1 + exp UA1 minus UA2( 1113857ε1113858 11138591113864 1113865 (33)

-e probability that the government node changes thestrategy is

pB 1

1 + exp UB1 minus UB2( 1113857ε1113858 11138591113864 1113865 (34)

UA1 UA2 UB1 and UB2 can be respectively obtained byequations (1)ndash(4) ε denotes the noise coefficient whichindicates the interference of uncontrollable factors such asexternal impact on the node updating strategy-e larger theε is the larger the interference is Generally ε 05 is taken

Finally the above game process is repeated until the stateof each node on the network reaches a stable state -esimulation is terminated and the simulation result isobtained

42 Basic Variable Settings of NetLogo Simulation Platform-is paper uses the NetLogo simulation platform to carryout evolutionary game simulation research on the complexnetwork NetLogo is a multisubject programmable modelingenvironment that can be applied for natural and socialphenomena It can control thousands of individuals inmodeling and can simulate the behavior of microindividualsthe emergence of macroscopic modes and their relation-ships which is especially suitable for simulating complexsystems that evolve over time

According to the algorithm steps of the evolutionarygame simulation on the complex network firstly the WSsmall-world network is generated and all the nodes on thenetwork are divided into the two categories of the residentand the government In the initial NetLogo interface theinitial parameters of the network can be determined byadjusting the sliders of each parameter as shown in Figure 3

In Figure 3 the relevant initial parameters of the modelare on the left side For example ldquonum-nodesrdquo indicates thenetwork scale namely the total number of subjects on thenetwork ldquoRewiring-probabilityrdquo indicates the randomreconnection probability p of the WS small-world networkldquoGovernment-of-total-nodesrdquo indicates the proportion ofthe government subjects on the network to the total subjectsldquoInitial-xrdquo indicates the proportion that the resident choosesrational negotiation strategies in the initial state ldquoInitial-yrdquoindicates the proportion that the government choosescompromised acceptance in the initial state ldquoCitizen-ratio-of-income-increaserdquo indicates the proportion of the residentto the increased total revenue of the project for the societyand ldquocitizen-ratio-of-costrdquo indicates the proportion of thegovernment to the total cost of the project ldquoTotal-income-increaserdquo indicates the increased total revenue of the projectfor the society ldquoTotal-costrdquo indicates the cost that ensuresthe project going smoothly ldquoCitizen-extra-income-forcerdquoindicates the additional revenue from the residentrsquos violent

Complexity 9

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

the resident and the government of the large-scale engi-neering projects is shown in Table 1

Assuming that the proportion of rational negotiationstrategy A1 adopted by the resident is x and that of com-promised acceptance strategy B1 adopted by the governmentis y the expected revenue of rational negotiation strategy A1and violent resistance strategy A2 adopted by resident arerespectively

UA1 yαR + RA minus βC (1)

UA2 RA + ΔRA minus ΔL (2)

-e expected revenue of the compromised acceptancestrategy B1 and tough control strategy B2 that the gov-ernment adopts are respectively

UB1 x(1 minus α)R + RB minus (1 minus β)C (3)

UB2 RB + ΔRB minus ΔS (4)

It can get that the expected revenue of the resident andthe government is respectivelyUA x yαR minus ΔRA minus βC + ΔL( 1113857 + RA + ΔRA minus ΔL

UB y x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 + RB + ΔRB minus ΔS

(5)

It can further get that the replicated dynamic equationsof the resident and government are respectively

dx

dt x(1 minus x) yαR minus ΔRA minus βC + ΔL( 1113857 (6)

dx

dt y(1 minus y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 (7)

In can be known from formula (6) that when x 0 1 or

y ΔRA + βC minus ΔL

αR (8)

the resident can achieve partial stability by adopting therational negotiation strategy from formula (7) when y 0 1or

x ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (9)

the government can adopt compromised acceptance strategyto achieve partial stability -us five partial equilibriumpoints are formed

E1(0 0) E2(1 0) E3(0 1) E4(1 1)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(10)

-e Jacobi matrix replicated can be obtained by repli-cated dynamic equations (6) and (7)

J (1 minus 2x) yαR minus ΔRA minus βC + ΔL( 1113857 x(1 minus x)αR

y(1 minus y)(1 minus α)R (1 minus 2y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 11138591113890 1113891 (11)

It can get that the determinants det J and tr J of the Jacobimatrix are respectively

detJ (1 minus 2x)(1 minus 2y) yαR minus ΔRA minus βC + ΔL( 1113857 x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859 minus xy(1 minus x)(1 minus y)αR(1 minus α)R

tr J (1 minus 2x) yαR minus ΔRA minus βC + ΔL( 1113857 +(1 minus 2y) x(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS1113858 1113859

(12)

Resident A

Government B

Rationalnegotiation A1

Violentresistance A2

Rational negotiationB1

Rational negotiationB1

Tough controlB2

Tough controlB2

RA + αR ndash βC RB + (1 ndash α)R ndash (1 ndash β)C RA ndash βC RB + ∆RB ndash ∆S RA + ∆RA ndash ∆L RB ndash (1 ndash β)C RA + ∆RA ndash ∆L RB + ∆RB ndash ∆S

Figure 1 Dynamic flow of evolutional game between the resident and the government in large-scale engineering projects

Complexity 5

It can get that the determinant and trace of the Jacobimatrix at five equilibrium points are shown in Table 2

Note T minus ΔRA + βC minus ΔL( 1113857 ΔRB +(1 minus β)C minus ΔS1113858 1113859 (1 minus α)R minus ΔRB +(1 minus β)C minus ΔS1113858 1113859 αR minus ΔRA + βC minus ΔL( 11138571113864 11138651113864 1113865

(1 minus α)RαR (13)

33 Multiscenario Evolutionary Game Analysis Afterobtaining the replication dynamic equation the next step isto analyze the evolutionary game equilibrium state of theresident and the government in the large-scale engineeringproject and its dynamic adjustment process under differentscenarios (the situation that the governmentrsquos extra stabilityexpenditures ΔS are different from the residentrsquos violentresistance cost ΔL)

331 Scenario One -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture and the residentrsquos violent resistance cost large then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

ΔLgt αRgtΔRA + βC(14)

Substituting above equations into the residentrsquo dynamicreplication equation (7) and the governmentrsquos replicationdynamic equation (8) it gets dxdtgt 0 dydtgt 0 In the 2 times

2 strategic space of the resident and the government theevolutionary phase map is shown in Figure 2(a) and theequilibrium result of the evolutionary game between theresident and the government is the only Nash equilibrium(rational negotiate A1 compromised acceptance B1)

When the governmentrsquos extra stability expenditure ΔSand the residentrsquos violent resistance cost ΔL are large boththe resident and the government will try to avoid adoptingstrategies that lead to deterioration of the situation (namelyviolent resistance and tough control) but will resolve con-flicts through rational negotiation in hope to gain the totalsocial revenue from the successful implementation of theproject

332 Scenario Two -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery small

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expenditure∆S and the residentrsquos violent resistance costΔL very small then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

αRgtΔRA + βCgtΔL(15)

For replication dynamic equation (6) of the resident if

ylowast

ΔRA + βC minus ΔL

αR (16)

then dxdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (17)

then dxdt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (18)

then dxdt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) of the government

if

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (19)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (20)

then dxdtgt 0 y⟶ 1 is the evolutionarily stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (21)

then dxdtlt 0 y⟶ 0 is the evolutionarily stable strategyIn the 2 times 2 strategic space between the government

and the resident by judging the positive and negativevalues of the determinant det J and the tr J of the fivepartial equilibrium points the points E1(0 0) and E4(1 1)

can be obtained as evolutionarily stable strategy thepoints E2(1 0) and E3(0 1) as unstable equilibriumpoints and the point

Table 1 -e payoff matrix of the evolutionary game between the resident and the government

Resident AGovernment B

Compromised acceptance B1 Tough control B2Rational negotiation A1 RA + αR minus βC RB + (1 minus α)R minus (1 minus β)C RA minus βC RB + ΔRB minus ΔSViolent resistance A2 RA + ΔRA minus ΔL RB minus (1 minus β)C RA + ΔRA minus ΔL RB + ΔRB minus ΔS

6 Complexity

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (22)

as unstable saddle points -e evolution phase diagram isshown in Figure 2(b)

When the governmentrsquos extra stability expenditure ∆Sand the residentrsquos violent resistance cost ΔL are very smallthe equilibrium result of the evolutionary game between theresident and the government in large-scale engineeringprojects is (rational negotiation A1 compromised accep-tance B1) or (violent resistanceA2 tough control B2) shownin Figure 2(b) -e specific evolutionary results are influ-enced by the initial state of social systems such as thestrength of the residentrsquos attitude to the large-scale engi-neering projects the expression manner of interest appeals

and the governmentrsquos ruling philosophy and the handlinghabits of the interest appeals When the initial state is locatedin region I and II in Figure 2(b) (namely quadrangleE1E2E5E3) evolution will converge to the point E1(0 0)then the resident adopts violent resistance strategy and thegovernment adopts tough control strategy When the initialstate is located in region III and IV in Figure 2(b) (namelyquadrangle E2E4E3E5) evolution will converge to the pointE4(1 1) then the resident adopts rational negotiationstrategy and the government adopts compromised accep-tance strategy

333 Scenario ree -e governmentrsquos extra stability ex-penditure ΔS is large and the residentrsquos violent resistancecost ΔL is small

Table 2 -e determinant and trace of the Jacobi matrix at five equilibrium points

Equilibriumpoint det J tr J

E1(00) (ΔRA + βC minus ΔL)[ΔRB + (1 minus β)C minus ΔS] minus (ΔRA + βC minus ΔL) minus [ΔR B + (1 minus β)C minus ΔS]

E2(10) (ΔRA + βC minus ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] (ΔRA + βC minus ΔL) + [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E3(01) (αR minus ΔRA minus βC + ΔL)[ΔRB + (1 minus β)C minus ΔS] (αR minus ΔRA minus βC + ΔL) + [ΔRB minus (1 minus β)C + ΔS]

E4(1 1) (αR minus ΔRA minus βC + ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] minus (αR minus ΔRA minus βC + ΔL) minus [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E5(xlowast ylowast) T 0

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

(a)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(b)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(c)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(d)

Figure 2 (a) -e equilibrium result when both ΔS and ΔL are large (b) the equilibrium result when both ΔS and ΔL are small (c) theequilibrium result when ΔS is large and ΔL is small (d) the equilibrium result when ΔS is small and ΔL is large

Complexity 7

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very large and the residentrsquos violent resistance cost∆L very small then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

αRgtΔRA + βCgtΔL(23)

For replication dynamic equation (6) when

ylowast

ΔRA + βC minus ΔL

αR (24)

then dtdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (25)

then dtdtgt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (26)

then dtdtlt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) nomatter what value xtakes dtdtgt 0 -erefore y⟶ 1 is the evolutionary stablestrategy

In the 2 times 2 strategic space between the government andthe resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the points E4(1 1) can be obtained asevolutionarily stable strategy points E1(0 0) E3(0 1) and

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (27)

as unstable saddle points and point E2(1 0) as unstablepoints -e evolution phase diagram is shown in Figure 2(c)

When the governmentrsquos extra stability expenditure ∆Sis large while the residentrsquos violent resistance cost ∆L issmall the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(c) Since thegovernmentrsquos extra stability expenditure is large thegovernment will try not to adopt tough control to increasespending but tend to adopt compromised acceptancestrategy At this time if the resident adopts violent resis-tance strategy they will increase their expenditure on theone hand (although the cost of violent resistance is small itis still greater than 0) and on the other hand asαRgtΔRA + βC αR minus βCgtΔRA is greater than 0 -e in-crease in revenue by adopting rational negotiation strategyis greater than that of the violent resistance strategy-erefore the resident will also tend to adopt the rationalnegotiation strategy

334 Scenario Four -e governmentrsquos extra stability ex-penditure ΔS is small and the residentrsquos violent resistancecost ΔL is large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very small and the residentrsquos violent resistance cost∆L very large then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

ΔLgt αRgtΔRA + βC(28)

For resident replication dynamic equation (6) no matterwhat value y takes dxdtgt 0 x⟶ 1 is the evolutionarystable strategy For government replication dynamic equa-tion (7) when

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (29)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (30)

then dxdtgt 0 y⟶ 1 is the evolutionary stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (31)

then dxdtlt 0 y⟶ 0 is the evolutionary stable strategyIn the 2 times 2 strategic space between the government and

the resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the point E4(1 1) is obtained as the evo-lutionary stable state points

E1(0 0) E2(1 0)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(32)

as unstable saddle points and point E3(0 1) as unstablepoints-e evolution phase diagram is shown in Figure 2(d)

When the governmentrsquos extra stability expenditure ∆Sis small and the residentrsquos violent resistance cost ∆L islarge the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(d) Since theresidentrsquos violent resistance cost is large the resident willtry not to adopt violent resistance to increase expenditurebut tend to adopt rational negotiation strategy At thistime if the government adopts tough control strategythey will increase their expenditure on the one hand(although the extra stability expenditure is small it is stillgreater than 0) and on the other hand as (1 minus α)RgtΔRB +

(1 minus β)C (1 minus α)RgtΔRB + (1 minus β)C is greater than 0 -eincrease in revenue by adopting compromised acceptancestrategy is greater than that of tough control strategy-erefore the government will also tend to adopt com-promised acceptance strategy

8 Complexity

4 Simulation Analysis of the Amplification ofStakeholder Conflict of Large-ScaleEngineering Projects on Complex Networks

41 Evolutionary Game Simulation Steps on ComplexNetworks Since Watts and Strogatz studied the averagepath length and clustering coefficient of the nematode neuralnetwork the American Western electrical power networkand the film actor cooperative network they found that ithad the characteristics of small world with average pathlength and large clustering coefficient and formally proposedthe small-world network [39] After long-term developmentthe small-world network has been proven to be effective inquantitatively studying the problems associated with com-plex social and economic systems -e network of multi-subject conflict amplification of large-scale engineeringprojects is essentially a complex network based on themultisubject interaction of realistic social networks andinfluenced by external systems such as social economicenvironment A large number of scholars studied the real-istic social network on the basis of complex networks andfound that its network topology had the characteristics ofsmall world with small average path length and largeclustering coefficient In view of the fact that the small-worldnetwork can help to explain problems related to complexsocial and economic systems and that the realistic com-munication network is similar to the small-world networkthe complex network structure type constructed in thispaper is a small-world network

For the simulation of the evolutionary game between theresident and the government in large-scale engineeringprojects on the complex network firstly we need to de-termine the strategic choice of individual players on thecomplex network then analyze the impact of differentnetwork characteristics on the evolutionary game resultsand explore the stakeholder conflict amplification mecha-nism of large-scale engineering projects

Firstly aWS small-world network with a certain numberof nodes is generated and network parameters are initial-ized All nodes on the network are divided into the twocategories of the resident and the government and theproportion of nodes on the network between the residentand the government is given -e meaning of the govern-ment includes all levels of governments government de-partments and officials related to the large-scale engineeringprojects -erefore the government is not only a node butshould also be regarded as multiple nodes on the networkand the number of which is much smaller than that of theresident nodes In the initial state the resident nodes ran-domly adopt the rational negotiation strategy A1 or theviolent resistance strategy A2 and the government noderandomly adopts the compromised acceptance strategy B1 orthe tough control strategy B2

Secondly in each round of the game each node on thecomplex network plays a game with all its neighbors and theresident and the government will change their own strategiesaccording to the updated rules after each round-e updatedrule is as follows the resident chooses to play games with its

neighbors if they are the same as the resident nodes thestrategy remains the same if they are government nodes andthe probability that the resident node changes the strategy is

pA 1

1 + exp UA1 minus UA2( 1113857ε1113858 11138591113864 1113865 (33)

-e probability that the government node changes thestrategy is

pB 1

1 + exp UB1 minus UB2( 1113857ε1113858 11138591113864 1113865 (34)

UA1 UA2 UB1 and UB2 can be respectively obtained byequations (1)ndash(4) ε denotes the noise coefficient whichindicates the interference of uncontrollable factors such asexternal impact on the node updating strategy-e larger theε is the larger the interference is Generally ε 05 is taken

Finally the above game process is repeated until the stateof each node on the network reaches a stable state -esimulation is terminated and the simulation result isobtained

42 Basic Variable Settings of NetLogo Simulation Platform-is paper uses the NetLogo simulation platform to carryout evolutionary game simulation research on the complexnetwork NetLogo is a multisubject programmable modelingenvironment that can be applied for natural and socialphenomena It can control thousands of individuals inmodeling and can simulate the behavior of microindividualsthe emergence of macroscopic modes and their relation-ships which is especially suitable for simulating complexsystems that evolve over time

According to the algorithm steps of the evolutionarygame simulation on the complex network firstly the WSsmall-world network is generated and all the nodes on thenetwork are divided into the two categories of the residentand the government In the initial NetLogo interface theinitial parameters of the network can be determined byadjusting the sliders of each parameter as shown in Figure 3

In Figure 3 the relevant initial parameters of the modelare on the left side For example ldquonum-nodesrdquo indicates thenetwork scale namely the total number of subjects on thenetwork ldquoRewiring-probabilityrdquo indicates the randomreconnection probability p of the WS small-world networkldquoGovernment-of-total-nodesrdquo indicates the proportion ofthe government subjects on the network to the total subjectsldquoInitial-xrdquo indicates the proportion that the resident choosesrational negotiation strategies in the initial state ldquoInitial-yrdquoindicates the proportion that the government choosescompromised acceptance in the initial state ldquoCitizen-ratio-of-income-increaserdquo indicates the proportion of the residentto the increased total revenue of the project for the societyand ldquocitizen-ratio-of-costrdquo indicates the proportion of thegovernment to the total cost of the project ldquoTotal-income-increaserdquo indicates the increased total revenue of the projectfor the society ldquoTotal-costrdquo indicates the cost that ensuresthe project going smoothly ldquoCitizen-extra-income-forcerdquoindicates the additional revenue from the residentrsquos violent

Complexity 9

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

It can get that the determinant and trace of the Jacobimatrix at five equilibrium points are shown in Table 2

Note T minus ΔRA + βC minus ΔL( 1113857 ΔRB +(1 minus β)C minus ΔS1113858 1113859 (1 minus α)R minus ΔRB +(1 minus β)C minus ΔS1113858 1113859 αR minus ΔRA + βC minus ΔL( 11138571113864 11138651113864 1113865

(1 minus α)RαR (13)

33 Multiscenario Evolutionary Game Analysis Afterobtaining the replication dynamic equation the next step isto analyze the evolutionary game equilibrium state of theresident and the government in the large-scale engineeringproject and its dynamic adjustment process under differentscenarios (the situation that the governmentrsquos extra stabilityexpenditures ΔS are different from the residentrsquos violentresistance cost ΔL)

331 Scenario One -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture and the residentrsquos violent resistance cost large then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

ΔLgt αRgtΔRA + βC(14)

Substituting above equations into the residentrsquo dynamicreplication equation (7) and the governmentrsquos replicationdynamic equation (8) it gets dxdtgt 0 dydtgt 0 In the 2 times

2 strategic space of the resident and the government theevolutionary phase map is shown in Figure 2(a) and theequilibrium result of the evolutionary game between theresident and the government is the only Nash equilibrium(rational negotiate A1 compromised acceptance B1)

When the governmentrsquos extra stability expenditure ΔSand the residentrsquos violent resistance cost ΔL are large boththe resident and the government will try to avoid adoptingstrategies that lead to deterioration of the situation (namelyviolent resistance and tough control) but will resolve con-flicts through rational negotiation in hope to gain the totalsocial revenue from the successful implementation of theproject

332 Scenario Two -e governmentrsquos extra stability ex-penditureΔS and the residentrsquos violent resistance cost ΔL arevery small

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expenditure∆S and the residentrsquos violent resistance costΔL very small then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

αRgtΔRA + βCgtΔL(15)

For replication dynamic equation (6) of the resident if

ylowast

ΔRA + βC minus ΔL

αR (16)

then dxdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (17)

then dxdt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (18)

then dxdt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) of the government

if

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (19)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (20)

then dxdtgt 0 y⟶ 1 is the evolutionarily stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (21)

then dxdtlt 0 y⟶ 0 is the evolutionarily stable strategyIn the 2 times 2 strategic space between the government

and the resident by judging the positive and negativevalues of the determinant det J and the tr J of the fivepartial equilibrium points the points E1(0 0) and E4(1 1)

can be obtained as evolutionarily stable strategy thepoints E2(1 0) and E3(0 1) as unstable equilibriumpoints and the point

Table 1 -e payoff matrix of the evolutionary game between the resident and the government

Resident AGovernment B

Compromised acceptance B1 Tough control B2Rational negotiation A1 RA + αR minus βC RB + (1 minus α)R minus (1 minus β)C RA minus βC RB + ΔRB minus ΔSViolent resistance A2 RA + ΔRA minus ΔL RB minus (1 minus β)C RA + ΔRA minus ΔL RB + ΔRB minus ΔS

6 Complexity

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (22)

as unstable saddle points -e evolution phase diagram isshown in Figure 2(b)

When the governmentrsquos extra stability expenditure ∆Sand the residentrsquos violent resistance cost ΔL are very smallthe equilibrium result of the evolutionary game between theresident and the government in large-scale engineeringprojects is (rational negotiation A1 compromised accep-tance B1) or (violent resistanceA2 tough control B2) shownin Figure 2(b) -e specific evolutionary results are influ-enced by the initial state of social systems such as thestrength of the residentrsquos attitude to the large-scale engi-neering projects the expression manner of interest appeals

and the governmentrsquos ruling philosophy and the handlinghabits of the interest appeals When the initial state is locatedin region I and II in Figure 2(b) (namely quadrangleE1E2E5E3) evolution will converge to the point E1(0 0)then the resident adopts violent resistance strategy and thegovernment adopts tough control strategy When the initialstate is located in region III and IV in Figure 2(b) (namelyquadrangle E2E4E3E5) evolution will converge to the pointE4(1 1) then the resident adopts rational negotiationstrategy and the government adopts compromised accep-tance strategy

333 Scenario ree -e governmentrsquos extra stability ex-penditure ΔS is large and the residentrsquos violent resistancecost ΔL is small

Table 2 -e determinant and trace of the Jacobi matrix at five equilibrium points

Equilibriumpoint det J tr J

E1(00) (ΔRA + βC minus ΔL)[ΔRB + (1 minus β)C minus ΔS] minus (ΔRA + βC minus ΔL) minus [ΔR B + (1 minus β)C minus ΔS]

E2(10) (ΔRA + βC minus ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] (ΔRA + βC minus ΔL) + [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E3(01) (αR minus ΔRA minus βC + ΔL)[ΔRB + (1 minus β)C minus ΔS] (αR minus ΔRA minus βC + ΔL) + [ΔRB minus (1 minus β)C + ΔS]

E4(1 1) (αR minus ΔRA minus βC + ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] minus (αR minus ΔRA minus βC + ΔL) minus [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E5(xlowast ylowast) T 0

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

(a)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(b)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(c)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(d)

Figure 2 (a) -e equilibrium result when both ΔS and ΔL are large (b) the equilibrium result when both ΔS and ΔL are small (c) theequilibrium result when ΔS is large and ΔL is small (d) the equilibrium result when ΔS is small and ΔL is large

Complexity 7

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very large and the residentrsquos violent resistance cost∆L very small then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

αRgtΔRA + βCgtΔL(23)

For replication dynamic equation (6) when

ylowast

ΔRA + βC minus ΔL

αR (24)

then dtdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (25)

then dtdtgt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (26)

then dtdtlt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) nomatter what value xtakes dtdtgt 0 -erefore y⟶ 1 is the evolutionary stablestrategy

In the 2 times 2 strategic space between the government andthe resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the points E4(1 1) can be obtained asevolutionarily stable strategy points E1(0 0) E3(0 1) and

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (27)

as unstable saddle points and point E2(1 0) as unstablepoints -e evolution phase diagram is shown in Figure 2(c)

When the governmentrsquos extra stability expenditure ∆Sis large while the residentrsquos violent resistance cost ∆L issmall the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(c) Since thegovernmentrsquos extra stability expenditure is large thegovernment will try not to adopt tough control to increasespending but tend to adopt compromised acceptancestrategy At this time if the resident adopts violent resis-tance strategy they will increase their expenditure on theone hand (although the cost of violent resistance is small itis still greater than 0) and on the other hand asαRgtΔRA + βC αR minus βCgtΔRA is greater than 0 -e in-crease in revenue by adopting rational negotiation strategyis greater than that of the violent resistance strategy-erefore the resident will also tend to adopt the rationalnegotiation strategy

334 Scenario Four -e governmentrsquos extra stability ex-penditure ΔS is small and the residentrsquos violent resistancecost ΔL is large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very small and the residentrsquos violent resistance cost∆L very large then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

ΔLgt αRgtΔRA + βC(28)

For resident replication dynamic equation (6) no matterwhat value y takes dxdtgt 0 x⟶ 1 is the evolutionarystable strategy For government replication dynamic equa-tion (7) when

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (29)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (30)

then dxdtgt 0 y⟶ 1 is the evolutionary stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (31)

then dxdtlt 0 y⟶ 0 is the evolutionary stable strategyIn the 2 times 2 strategic space between the government and

the resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the point E4(1 1) is obtained as the evo-lutionary stable state points

E1(0 0) E2(1 0)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(32)

as unstable saddle points and point E3(0 1) as unstablepoints-e evolution phase diagram is shown in Figure 2(d)

When the governmentrsquos extra stability expenditure ∆Sis small and the residentrsquos violent resistance cost ∆L islarge the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(d) Since theresidentrsquos violent resistance cost is large the resident willtry not to adopt violent resistance to increase expenditurebut tend to adopt rational negotiation strategy At thistime if the government adopts tough control strategythey will increase their expenditure on the one hand(although the extra stability expenditure is small it is stillgreater than 0) and on the other hand as (1 minus α)RgtΔRB +

(1 minus β)C (1 minus α)RgtΔRB + (1 minus β)C is greater than 0 -eincrease in revenue by adopting compromised acceptancestrategy is greater than that of tough control strategy-erefore the government will also tend to adopt com-promised acceptance strategy

8 Complexity

4 Simulation Analysis of the Amplification ofStakeholder Conflict of Large-ScaleEngineering Projects on Complex Networks

41 Evolutionary Game Simulation Steps on ComplexNetworks Since Watts and Strogatz studied the averagepath length and clustering coefficient of the nematode neuralnetwork the American Western electrical power networkand the film actor cooperative network they found that ithad the characteristics of small world with average pathlength and large clustering coefficient and formally proposedthe small-world network [39] After long-term developmentthe small-world network has been proven to be effective inquantitatively studying the problems associated with com-plex social and economic systems -e network of multi-subject conflict amplification of large-scale engineeringprojects is essentially a complex network based on themultisubject interaction of realistic social networks andinfluenced by external systems such as social economicenvironment A large number of scholars studied the real-istic social network on the basis of complex networks andfound that its network topology had the characteristics ofsmall world with small average path length and largeclustering coefficient In view of the fact that the small-worldnetwork can help to explain problems related to complexsocial and economic systems and that the realistic com-munication network is similar to the small-world networkthe complex network structure type constructed in thispaper is a small-world network

For the simulation of the evolutionary game between theresident and the government in large-scale engineeringprojects on the complex network firstly we need to de-termine the strategic choice of individual players on thecomplex network then analyze the impact of differentnetwork characteristics on the evolutionary game resultsand explore the stakeholder conflict amplification mecha-nism of large-scale engineering projects

Firstly aWS small-world network with a certain numberof nodes is generated and network parameters are initial-ized All nodes on the network are divided into the twocategories of the resident and the government and theproportion of nodes on the network between the residentand the government is given -e meaning of the govern-ment includes all levels of governments government de-partments and officials related to the large-scale engineeringprojects -erefore the government is not only a node butshould also be regarded as multiple nodes on the networkand the number of which is much smaller than that of theresident nodes In the initial state the resident nodes ran-domly adopt the rational negotiation strategy A1 or theviolent resistance strategy A2 and the government noderandomly adopts the compromised acceptance strategy B1 orthe tough control strategy B2

Secondly in each round of the game each node on thecomplex network plays a game with all its neighbors and theresident and the government will change their own strategiesaccording to the updated rules after each round-e updatedrule is as follows the resident chooses to play games with its

neighbors if they are the same as the resident nodes thestrategy remains the same if they are government nodes andthe probability that the resident node changes the strategy is

pA 1

1 + exp UA1 minus UA2( 1113857ε1113858 11138591113864 1113865 (33)

-e probability that the government node changes thestrategy is

pB 1

1 + exp UB1 minus UB2( 1113857ε1113858 11138591113864 1113865 (34)

UA1 UA2 UB1 and UB2 can be respectively obtained byequations (1)ndash(4) ε denotes the noise coefficient whichindicates the interference of uncontrollable factors such asexternal impact on the node updating strategy-e larger theε is the larger the interference is Generally ε 05 is taken

Finally the above game process is repeated until the stateof each node on the network reaches a stable state -esimulation is terminated and the simulation result isobtained

42 Basic Variable Settings of NetLogo Simulation Platform-is paper uses the NetLogo simulation platform to carryout evolutionary game simulation research on the complexnetwork NetLogo is a multisubject programmable modelingenvironment that can be applied for natural and socialphenomena It can control thousands of individuals inmodeling and can simulate the behavior of microindividualsthe emergence of macroscopic modes and their relation-ships which is especially suitable for simulating complexsystems that evolve over time

According to the algorithm steps of the evolutionarygame simulation on the complex network firstly the WSsmall-world network is generated and all the nodes on thenetwork are divided into the two categories of the residentand the government In the initial NetLogo interface theinitial parameters of the network can be determined byadjusting the sliders of each parameter as shown in Figure 3

In Figure 3 the relevant initial parameters of the modelare on the left side For example ldquonum-nodesrdquo indicates thenetwork scale namely the total number of subjects on thenetwork ldquoRewiring-probabilityrdquo indicates the randomreconnection probability p of the WS small-world networkldquoGovernment-of-total-nodesrdquo indicates the proportion ofthe government subjects on the network to the total subjectsldquoInitial-xrdquo indicates the proportion that the resident choosesrational negotiation strategies in the initial state ldquoInitial-yrdquoindicates the proportion that the government choosescompromised acceptance in the initial state ldquoCitizen-ratio-of-income-increaserdquo indicates the proportion of the residentto the increased total revenue of the project for the societyand ldquocitizen-ratio-of-costrdquo indicates the proportion of thegovernment to the total cost of the project ldquoTotal-income-increaserdquo indicates the increased total revenue of the projectfor the society ldquoTotal-costrdquo indicates the cost that ensuresthe project going smoothly ldquoCitizen-extra-income-forcerdquoindicates the additional revenue from the residentrsquos violent

Complexity 9

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (22)

as unstable saddle points -e evolution phase diagram isshown in Figure 2(b)

When the governmentrsquos extra stability expenditure ∆Sand the residentrsquos violent resistance cost ΔL are very smallthe equilibrium result of the evolutionary game between theresident and the government in large-scale engineeringprojects is (rational negotiation A1 compromised accep-tance B1) or (violent resistanceA2 tough control B2) shownin Figure 2(b) -e specific evolutionary results are influ-enced by the initial state of social systems such as thestrength of the residentrsquos attitude to the large-scale engi-neering projects the expression manner of interest appeals

and the governmentrsquos ruling philosophy and the handlinghabits of the interest appeals When the initial state is locatedin region I and II in Figure 2(b) (namely quadrangleE1E2E5E3) evolution will converge to the point E1(0 0)then the resident adopts violent resistance strategy and thegovernment adopts tough control strategy When the initialstate is located in region III and IV in Figure 2(b) (namelyquadrangle E2E4E3E5) evolution will converge to the pointE4(1 1) then the resident adopts rational negotiationstrategy and the government adopts compromised accep-tance strategy

333 Scenario ree -e governmentrsquos extra stability ex-penditure ΔS is large and the residentrsquos violent resistancecost ΔL is small

Table 2 -e determinant and trace of the Jacobi matrix at five equilibrium points

Equilibriumpoint det J tr J

E1(00) (ΔRA + βC minus ΔL)[ΔRB + (1 minus β)C minus ΔS] minus (ΔRA + βC minus ΔL) minus [ΔR B + (1 minus β)C minus ΔS]

E2(10) (ΔRA + βC minus ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] (ΔRA + βC minus ΔL) + [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E3(01) (αR minus ΔRA minus βC + ΔL)[ΔRB + (1 minus β)C minus ΔS] (αR minus ΔRA minus βC + ΔL) + [ΔRB minus (1 minus β)C + ΔS]

E4(1 1) (αR minus ΔRA minus βC + ΔL)[(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS] minus (αR minus ΔRA minus βC + ΔL) minus [(1 minus α)R minus ΔRB minus (1 minus β)C + ΔS]

E5(xlowast ylowast) T 0

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

(a)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(b)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(c)

y

E3 (0 1) E4 (1 1)

E1 (0 0) E2 (1 0)x

IV

II

I IIIE5

(d)

Figure 2 (a) -e equilibrium result when both ΔS and ΔL are large (b) the equilibrium result when both ΔS and ΔL are small (c) theequilibrium result when ΔS is large and ΔL is small (d) the equilibrium result when ΔS is small and ΔL is large

Complexity 7

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very large and the residentrsquos violent resistance cost∆L very small then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

αRgtΔRA + βCgtΔL(23)

For replication dynamic equation (6) when

ylowast

ΔRA + βC minus ΔL

αR (24)

then dtdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (25)

then dtdtgt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (26)

then dtdtlt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) nomatter what value xtakes dtdtgt 0 -erefore y⟶ 1 is the evolutionary stablestrategy

In the 2 times 2 strategic space between the government andthe resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the points E4(1 1) can be obtained asevolutionarily stable strategy points E1(0 0) E3(0 1) and

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (27)

as unstable saddle points and point E2(1 0) as unstablepoints -e evolution phase diagram is shown in Figure 2(c)

When the governmentrsquos extra stability expenditure ∆Sis large while the residentrsquos violent resistance cost ∆L issmall the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(c) Since thegovernmentrsquos extra stability expenditure is large thegovernment will try not to adopt tough control to increasespending but tend to adopt compromised acceptancestrategy At this time if the resident adopts violent resis-tance strategy they will increase their expenditure on theone hand (although the cost of violent resistance is small itis still greater than 0) and on the other hand asαRgtΔRA + βC αR minus βCgtΔRA is greater than 0 -e in-crease in revenue by adopting rational negotiation strategyis greater than that of the violent resistance strategy-erefore the resident will also tend to adopt the rationalnegotiation strategy

334 Scenario Four -e governmentrsquos extra stability ex-penditure ΔS is small and the residentrsquos violent resistancecost ΔL is large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very small and the residentrsquos violent resistance cost∆L very large then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

ΔLgt αRgtΔRA + βC(28)

For resident replication dynamic equation (6) no matterwhat value y takes dxdtgt 0 x⟶ 1 is the evolutionarystable strategy For government replication dynamic equa-tion (7) when

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (29)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (30)

then dxdtgt 0 y⟶ 1 is the evolutionary stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (31)

then dxdtlt 0 y⟶ 0 is the evolutionary stable strategyIn the 2 times 2 strategic space between the government and

the resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the point E4(1 1) is obtained as the evo-lutionary stable state points

E1(0 0) E2(1 0)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(32)

as unstable saddle points and point E3(0 1) as unstablepoints-e evolution phase diagram is shown in Figure 2(d)

When the governmentrsquos extra stability expenditure ∆Sis small and the residentrsquos violent resistance cost ∆L islarge the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(d) Since theresidentrsquos violent resistance cost is large the resident willtry not to adopt violent resistance to increase expenditurebut tend to adopt rational negotiation strategy At thistime if the government adopts tough control strategythey will increase their expenditure on the one hand(although the extra stability expenditure is small it is stillgreater than 0) and on the other hand as (1 minus α)RgtΔRB +

(1 minus β)C (1 minus α)RgtΔRB + (1 minus β)C is greater than 0 -eincrease in revenue by adopting compromised acceptancestrategy is greater than that of tough control strategy-erefore the government will also tend to adopt com-promised acceptance strategy

8 Complexity

4 Simulation Analysis of the Amplification ofStakeholder Conflict of Large-ScaleEngineering Projects on Complex Networks

41 Evolutionary Game Simulation Steps on ComplexNetworks Since Watts and Strogatz studied the averagepath length and clustering coefficient of the nematode neuralnetwork the American Western electrical power networkand the film actor cooperative network they found that ithad the characteristics of small world with average pathlength and large clustering coefficient and formally proposedthe small-world network [39] After long-term developmentthe small-world network has been proven to be effective inquantitatively studying the problems associated with com-plex social and economic systems -e network of multi-subject conflict amplification of large-scale engineeringprojects is essentially a complex network based on themultisubject interaction of realistic social networks andinfluenced by external systems such as social economicenvironment A large number of scholars studied the real-istic social network on the basis of complex networks andfound that its network topology had the characteristics ofsmall world with small average path length and largeclustering coefficient In view of the fact that the small-worldnetwork can help to explain problems related to complexsocial and economic systems and that the realistic com-munication network is similar to the small-world networkthe complex network structure type constructed in thispaper is a small-world network

For the simulation of the evolutionary game between theresident and the government in large-scale engineeringprojects on the complex network firstly we need to de-termine the strategic choice of individual players on thecomplex network then analyze the impact of differentnetwork characteristics on the evolutionary game resultsand explore the stakeholder conflict amplification mecha-nism of large-scale engineering projects

Firstly aWS small-world network with a certain numberof nodes is generated and network parameters are initial-ized All nodes on the network are divided into the twocategories of the resident and the government and theproportion of nodes on the network between the residentand the government is given -e meaning of the govern-ment includes all levels of governments government de-partments and officials related to the large-scale engineeringprojects -erefore the government is not only a node butshould also be regarded as multiple nodes on the networkand the number of which is much smaller than that of theresident nodes In the initial state the resident nodes ran-domly adopt the rational negotiation strategy A1 or theviolent resistance strategy A2 and the government noderandomly adopts the compromised acceptance strategy B1 orthe tough control strategy B2

Secondly in each round of the game each node on thecomplex network plays a game with all its neighbors and theresident and the government will change their own strategiesaccording to the updated rules after each round-e updatedrule is as follows the resident chooses to play games with its

neighbors if they are the same as the resident nodes thestrategy remains the same if they are government nodes andthe probability that the resident node changes the strategy is

pA 1

1 + exp UA1 minus UA2( 1113857ε1113858 11138591113864 1113865 (33)

-e probability that the government node changes thestrategy is

pB 1

1 + exp UB1 minus UB2( 1113857ε1113858 11138591113864 1113865 (34)

UA1 UA2 UB1 and UB2 can be respectively obtained byequations (1)ndash(4) ε denotes the noise coefficient whichindicates the interference of uncontrollable factors such asexternal impact on the node updating strategy-e larger theε is the larger the interference is Generally ε 05 is taken

Finally the above game process is repeated until the stateof each node on the network reaches a stable state -esimulation is terminated and the simulation result isobtained

42 Basic Variable Settings of NetLogo Simulation Platform-is paper uses the NetLogo simulation platform to carryout evolutionary game simulation research on the complexnetwork NetLogo is a multisubject programmable modelingenvironment that can be applied for natural and socialphenomena It can control thousands of individuals inmodeling and can simulate the behavior of microindividualsthe emergence of macroscopic modes and their relation-ships which is especially suitable for simulating complexsystems that evolve over time

According to the algorithm steps of the evolutionarygame simulation on the complex network firstly the WSsmall-world network is generated and all the nodes on thenetwork are divided into the two categories of the residentand the government In the initial NetLogo interface theinitial parameters of the network can be determined byadjusting the sliders of each parameter as shown in Figure 3

In Figure 3 the relevant initial parameters of the modelare on the left side For example ldquonum-nodesrdquo indicates thenetwork scale namely the total number of subjects on thenetwork ldquoRewiring-probabilityrdquo indicates the randomreconnection probability p of the WS small-world networkldquoGovernment-of-total-nodesrdquo indicates the proportion ofthe government subjects on the network to the total subjectsldquoInitial-xrdquo indicates the proportion that the resident choosesrational negotiation strategies in the initial state ldquoInitial-yrdquoindicates the proportion that the government choosescompromised acceptance in the initial state ldquoCitizen-ratio-of-income-increaserdquo indicates the proportion of the residentto the increased total revenue of the project for the societyand ldquocitizen-ratio-of-costrdquo indicates the proportion of thegovernment to the total cost of the project ldquoTotal-income-increaserdquo indicates the increased total revenue of the projectfor the society ldquoTotal-costrdquo indicates the cost that ensuresthe project going smoothly ldquoCitizen-extra-income-forcerdquoindicates the additional revenue from the residentrsquos violent

Complexity 9

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very large and the residentrsquos violent resistance cost∆L very small then

ΔSgt(1 minus α)RgtΔRB +(1 minus β)C

αRgtΔRA + βCgtΔL(23)

For replication dynamic equation (6) when

ylowast

ΔRA + βC minus ΔL

αR (24)

then dtdt 0 0ltylowast lt 1 is the mixed equilibrium pointWhen

ygtΔRA + βC minus ΔL

αR (25)

then dtdtgt 0 x⟶ 1 is the evolutionarily stable strategyWhen

yltΔRA + βC minus ΔL

αR (26)

then dtdtlt 0 x⟶ 0 is the evolutionarily stable strategyFor replication dynamic equation (7) nomatter what value xtakes dtdtgt 0 -erefore y⟶ 1 is the evolutionary stablestrategy

In the 2 times 2 strategic space between the government andthe resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the points E4(1 1) can be obtained asevolutionarily stable strategy points E1(0 0) E3(0 1) and

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889 (27)

as unstable saddle points and point E2(1 0) as unstablepoints -e evolution phase diagram is shown in Figure 2(c)

When the governmentrsquos extra stability expenditure ∆Sis large while the residentrsquos violent resistance cost ∆L issmall the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(c) Since thegovernmentrsquos extra stability expenditure is large thegovernment will try not to adopt tough control to increasespending but tend to adopt compromised acceptancestrategy At this time if the resident adopts violent resis-tance strategy they will increase their expenditure on theone hand (although the cost of violent resistance is small itis still greater than 0) and on the other hand asαRgtΔRA + βC αR minus βCgtΔRA is greater than 0 -e in-crease in revenue by adopting rational negotiation strategyis greater than that of the violent resistance strategy-erefore the resident will also tend to adopt the rationalnegotiation strategy

334 Scenario Four -e governmentrsquos extra stability ex-penditure ΔS is small and the residentrsquos violent resistancecost ΔL is large

If both the resident and the government adopt toughstrategies causing the governmentrsquos extra stability expen-diture ∆S very small and the residentrsquos violent resistance cost∆L very large then

(1 minus α)RgtΔRB +(1 minus β)CgtΔS

ΔLgt αRgtΔRA + βC(28)

For resident replication dynamic equation (6) no matterwhat value y takes dxdtgt 0 x⟶ 1 is the evolutionarystable strategy For government replication dynamic equa-tion (7) when

xlowast

ΔRB +(1 minus β)C minus ΔS

(1 minus α)R (29)

then dxdt 0 0ltxlowast lt 1 is the mixed equilibrium pointWhen

xgtΔRB +(1 minus β)C minus ΔS

(1 minus α)R (30)

then dxdtgt 0 y⟶ 1 is the evolutionary stable strategyWhen

xltΔRB +(1 minus β)C minus ΔS

(1 minus α)R (31)

then dxdtlt 0 y⟶ 0 is the evolutionary stable strategyIn the 2 times 2 strategic space between the government and

the resident by judging the positive and negative values ofthe determinant det J and the tr J of the five partial equi-librium points the point E4(1 1) is obtained as the evo-lutionary stable state points

E1(0 0) E2(1 0)

E5ΔRB +(1 minus β)C minus ΔS

(1 minus α)RΔRA + βC minus ΔL

αR1113888 1113889

(32)

as unstable saddle points and point E3(0 1) as unstablepoints-e evolution phase diagram is shown in Figure 2(d)

When the governmentrsquos extra stability expenditure ∆Sis small and the residentrsquos violent resistance cost ∆L islarge the equilibrium result of the evolutionary gamebetween the resident and the government in large-scaleengineering projects is (national negotiation A1 com-promised acceptance B1) shown in Figure 2(d) Since theresidentrsquos violent resistance cost is large the resident willtry not to adopt violent resistance to increase expenditurebut tend to adopt rational negotiation strategy At thistime if the government adopts tough control strategythey will increase their expenditure on the one hand(although the extra stability expenditure is small it is stillgreater than 0) and on the other hand as (1 minus α)RgtΔRB +

(1 minus β)C (1 minus α)RgtΔRB + (1 minus β)C is greater than 0 -eincrease in revenue by adopting compromised acceptancestrategy is greater than that of tough control strategy-erefore the government will also tend to adopt com-promised acceptance strategy

8 Complexity

4 Simulation Analysis of the Amplification ofStakeholder Conflict of Large-ScaleEngineering Projects on Complex Networks

41 Evolutionary Game Simulation Steps on ComplexNetworks Since Watts and Strogatz studied the averagepath length and clustering coefficient of the nematode neuralnetwork the American Western electrical power networkand the film actor cooperative network they found that ithad the characteristics of small world with average pathlength and large clustering coefficient and formally proposedthe small-world network [39] After long-term developmentthe small-world network has been proven to be effective inquantitatively studying the problems associated with com-plex social and economic systems -e network of multi-subject conflict amplification of large-scale engineeringprojects is essentially a complex network based on themultisubject interaction of realistic social networks andinfluenced by external systems such as social economicenvironment A large number of scholars studied the real-istic social network on the basis of complex networks andfound that its network topology had the characteristics ofsmall world with small average path length and largeclustering coefficient In view of the fact that the small-worldnetwork can help to explain problems related to complexsocial and economic systems and that the realistic com-munication network is similar to the small-world networkthe complex network structure type constructed in thispaper is a small-world network

For the simulation of the evolutionary game between theresident and the government in large-scale engineeringprojects on the complex network firstly we need to de-termine the strategic choice of individual players on thecomplex network then analyze the impact of differentnetwork characteristics on the evolutionary game resultsand explore the stakeholder conflict amplification mecha-nism of large-scale engineering projects

Firstly aWS small-world network with a certain numberof nodes is generated and network parameters are initial-ized All nodes on the network are divided into the twocategories of the resident and the government and theproportion of nodes on the network between the residentand the government is given -e meaning of the govern-ment includes all levels of governments government de-partments and officials related to the large-scale engineeringprojects -erefore the government is not only a node butshould also be regarded as multiple nodes on the networkand the number of which is much smaller than that of theresident nodes In the initial state the resident nodes ran-domly adopt the rational negotiation strategy A1 or theviolent resistance strategy A2 and the government noderandomly adopts the compromised acceptance strategy B1 orthe tough control strategy B2

Secondly in each round of the game each node on thecomplex network plays a game with all its neighbors and theresident and the government will change their own strategiesaccording to the updated rules after each round-e updatedrule is as follows the resident chooses to play games with its

neighbors if they are the same as the resident nodes thestrategy remains the same if they are government nodes andthe probability that the resident node changes the strategy is

pA 1

1 + exp UA1 minus UA2( 1113857ε1113858 11138591113864 1113865 (33)

-e probability that the government node changes thestrategy is

pB 1

1 + exp UB1 minus UB2( 1113857ε1113858 11138591113864 1113865 (34)

UA1 UA2 UB1 and UB2 can be respectively obtained byequations (1)ndash(4) ε denotes the noise coefficient whichindicates the interference of uncontrollable factors such asexternal impact on the node updating strategy-e larger theε is the larger the interference is Generally ε 05 is taken

Finally the above game process is repeated until the stateof each node on the network reaches a stable state -esimulation is terminated and the simulation result isobtained

42 Basic Variable Settings of NetLogo Simulation Platform-is paper uses the NetLogo simulation platform to carryout evolutionary game simulation research on the complexnetwork NetLogo is a multisubject programmable modelingenvironment that can be applied for natural and socialphenomena It can control thousands of individuals inmodeling and can simulate the behavior of microindividualsthe emergence of macroscopic modes and their relation-ships which is especially suitable for simulating complexsystems that evolve over time

According to the algorithm steps of the evolutionarygame simulation on the complex network firstly the WSsmall-world network is generated and all the nodes on thenetwork are divided into the two categories of the residentand the government In the initial NetLogo interface theinitial parameters of the network can be determined byadjusting the sliders of each parameter as shown in Figure 3

In Figure 3 the relevant initial parameters of the modelare on the left side For example ldquonum-nodesrdquo indicates thenetwork scale namely the total number of subjects on thenetwork ldquoRewiring-probabilityrdquo indicates the randomreconnection probability p of the WS small-world networkldquoGovernment-of-total-nodesrdquo indicates the proportion ofthe government subjects on the network to the total subjectsldquoInitial-xrdquo indicates the proportion that the resident choosesrational negotiation strategies in the initial state ldquoInitial-yrdquoindicates the proportion that the government choosescompromised acceptance in the initial state ldquoCitizen-ratio-of-income-increaserdquo indicates the proportion of the residentto the increased total revenue of the project for the societyand ldquocitizen-ratio-of-costrdquo indicates the proportion of thegovernment to the total cost of the project ldquoTotal-income-increaserdquo indicates the increased total revenue of the projectfor the society ldquoTotal-costrdquo indicates the cost that ensuresthe project going smoothly ldquoCitizen-extra-income-forcerdquoindicates the additional revenue from the residentrsquos violent

Complexity 9

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

4 Simulation Analysis of the Amplification ofStakeholder Conflict of Large-ScaleEngineering Projects on Complex Networks

41 Evolutionary Game Simulation Steps on ComplexNetworks Since Watts and Strogatz studied the averagepath length and clustering coefficient of the nematode neuralnetwork the American Western electrical power networkand the film actor cooperative network they found that ithad the characteristics of small world with average pathlength and large clustering coefficient and formally proposedthe small-world network [39] After long-term developmentthe small-world network has been proven to be effective inquantitatively studying the problems associated with com-plex social and economic systems -e network of multi-subject conflict amplification of large-scale engineeringprojects is essentially a complex network based on themultisubject interaction of realistic social networks andinfluenced by external systems such as social economicenvironment A large number of scholars studied the real-istic social network on the basis of complex networks andfound that its network topology had the characteristics ofsmall world with small average path length and largeclustering coefficient In view of the fact that the small-worldnetwork can help to explain problems related to complexsocial and economic systems and that the realistic com-munication network is similar to the small-world networkthe complex network structure type constructed in thispaper is a small-world network

For the simulation of the evolutionary game between theresident and the government in large-scale engineeringprojects on the complex network firstly we need to de-termine the strategic choice of individual players on thecomplex network then analyze the impact of differentnetwork characteristics on the evolutionary game resultsand explore the stakeholder conflict amplification mecha-nism of large-scale engineering projects

Firstly aWS small-world network with a certain numberof nodes is generated and network parameters are initial-ized All nodes on the network are divided into the twocategories of the resident and the government and theproportion of nodes on the network between the residentand the government is given -e meaning of the govern-ment includes all levels of governments government de-partments and officials related to the large-scale engineeringprojects -erefore the government is not only a node butshould also be regarded as multiple nodes on the networkand the number of which is much smaller than that of theresident nodes In the initial state the resident nodes ran-domly adopt the rational negotiation strategy A1 or theviolent resistance strategy A2 and the government noderandomly adopts the compromised acceptance strategy B1 orthe tough control strategy B2

Secondly in each round of the game each node on thecomplex network plays a game with all its neighbors and theresident and the government will change their own strategiesaccording to the updated rules after each round-e updatedrule is as follows the resident chooses to play games with its

neighbors if they are the same as the resident nodes thestrategy remains the same if they are government nodes andthe probability that the resident node changes the strategy is

pA 1

1 + exp UA1 minus UA2( 1113857ε1113858 11138591113864 1113865 (33)

-e probability that the government node changes thestrategy is

pB 1

1 + exp UB1 minus UB2( 1113857ε1113858 11138591113864 1113865 (34)

UA1 UA2 UB1 and UB2 can be respectively obtained byequations (1)ndash(4) ε denotes the noise coefficient whichindicates the interference of uncontrollable factors such asexternal impact on the node updating strategy-e larger theε is the larger the interference is Generally ε 05 is taken

Finally the above game process is repeated until the stateof each node on the network reaches a stable state -esimulation is terminated and the simulation result isobtained

42 Basic Variable Settings of NetLogo Simulation Platform-is paper uses the NetLogo simulation platform to carryout evolutionary game simulation research on the complexnetwork NetLogo is a multisubject programmable modelingenvironment that can be applied for natural and socialphenomena It can control thousands of individuals inmodeling and can simulate the behavior of microindividualsthe emergence of macroscopic modes and their relation-ships which is especially suitable for simulating complexsystems that evolve over time

According to the algorithm steps of the evolutionarygame simulation on the complex network firstly the WSsmall-world network is generated and all the nodes on thenetwork are divided into the two categories of the residentand the government In the initial NetLogo interface theinitial parameters of the network can be determined byadjusting the sliders of each parameter as shown in Figure 3

In Figure 3 the relevant initial parameters of the modelare on the left side For example ldquonum-nodesrdquo indicates thenetwork scale namely the total number of subjects on thenetwork ldquoRewiring-probabilityrdquo indicates the randomreconnection probability p of the WS small-world networkldquoGovernment-of-total-nodesrdquo indicates the proportion ofthe government subjects on the network to the total subjectsldquoInitial-xrdquo indicates the proportion that the resident choosesrational negotiation strategies in the initial state ldquoInitial-yrdquoindicates the proportion that the government choosescompromised acceptance in the initial state ldquoCitizen-ratio-of-income-increaserdquo indicates the proportion of the residentto the increased total revenue of the project for the societyand ldquocitizen-ratio-of-costrdquo indicates the proportion of thegovernment to the total cost of the project ldquoTotal-income-increaserdquo indicates the increased total revenue of the projectfor the society ldquoTotal-costrdquo indicates the cost that ensuresthe project going smoothly ldquoCitizen-extra-income-forcerdquoindicates the additional revenue from the residentrsquos violent

Complexity 9

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

resistance ldquoGovernment-extra-income-forcerdquo indicates theadditional revenue from the governmentrsquos tough controlldquoCitizen-cost-forcerdquo indicates the cost of the residentrsquos vi-olent resistance ldquoGovernment-cost-forcerdquo indicates addi-tional expenditure from the governmentrsquos tough control-e right side of the figure represents the generated networkwhere ldquopeoplerdquo indicates the resident and ldquofive-pointed starrdquorepresents the government Among the resident subjects thegreen indicates those who choose rational negotiationstrategy and the blue indicates those who choose violentresistance strategy Among the government subjects the redindicates those who choose compromised acceptancestrategy and the yellow indicates those who choose toughcontrol strategy

In the initial state it is assumed that the reconnectionprobability p of small-world networks is 02 the number ofsubjects on the whole network is 100 to which the proportionof the government subjects is 02 the proportion x of theresident who adopts rational negotiation strategy is 03 theproportion y of the government who adopts compromisedacceptance strategy is 05 the increased proportion α of theresident to the total revenue is 03 the proportion β of the totalcost that the resident share is 02 the increased total revenue Ris 100 the total cost C is 40 the initial retained revenue of theresident RA is 10 the initial retained revenue of the gov-ernment RB is 10 the additional revenue ΔRA obtained by theresidentrsquos violent resistance is 20 and the additional revenueΔRB obtained by the governmentrsquos tough control is 20

43 Simulation Result andAnalysis -is paper will simulatethe evolutionary game results of the government and the

resident on the small-world network under different sce-narios and analyze the impact of different initial states anddifferent network characteristics on the conflicts between thegovernment and the resident subjects in large-scale engi-neering projects With the start of the simulation the colorof the subjects in the network diagram on the right side ofFigure 3 will gradually change with the start of the game andthe result will also be displayed in the lower left corner ofFigure 3 on the ldquoNetworkStatusrdquo -e abscissa indicates theevolution time and the ordinate indicates the proportion ofthe rational resident -e green indicates the proportion ofthe resident who chooses rational negotiation and the redindicates the proportion of the government who choosescompromised acceptance

431 Scenario One -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L arevery large

In scenario one the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)CΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 4

It can be seen from Figure 4 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibrium

(a) (b)

Figure 3 -e initial state on the WS small-world network

10 Complexity

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

tends to (rational negotiation compromise acceptance) butwith the increase of reconnection probability the time thatthey evolve to a stable state has been significantly reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0395 0261 0181 and 0156 and the averagepath length is respectively 2054 1962 1905 and 1893which indicates that with the increase of reconnectionprobability of the small-world network the clustering co-efficient and the average path length decrease -e decreaseof the clustering coefficient indicates that the concentrationdegree of the conflict network between the resident and thegovernment gets low showing a decentralized state and theheterogeneity among subjects is more prominent Somesubjects with large nodes have greater influence than othersubjects thus easier to reach the equilibrium state -edecrease of the average path length indicates that the scale ofthe network between the resident and the government getssmall the interaction closeness among the subjects getsincreased and it is easier to achieve equilibrium state

432 Scenario Two -e governmentrsquos extra stability ex-penditure ∆S and the residentrsquos violent resistance cost ∆L aresmall

In scenario two the condition (1 minus α)RgtΔRB+

(1 minus β)CgtΔS αRgtΔRA + βCgtΔL is satisfied and the

assumed parameter is set as follows the residentrsquos violentresistance cost ΔL is 10 and the governmentrsquos extra stabilityexpenditure ∆S of tough control is 20 When the recon-nection probability p of the small-world network takesdifferent values the evolutionary results of the game be-tween the resident and the government are shown inFigure 5

It can be seen from Figure 5 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (violent resistance tough control) but with theincrease of reconnection probability the time that theyevolve to a relatively stable state has been gradually reducedWhen the reconnection probability p is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0416 0233 018 and 0155 and the average pathlength is respectively 208 1931 1907 and 1895 Similarto scenario one it also shows that with the increase ofreconnection probability of the small-world network theclustering coefficient and the average path length decreasemaking the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

In the previous analysis we know that the proportion xthat the resident adopts rational negotiation is 03 and theproportion y that the government adopts compromised

(a) (b)

(c) (d)

Figure 4 -e evolutionary results when the reconnection probability p takes different values in scenario one (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 11

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

acceptance is 05 and the state at this time is in region I andII of Figure 2(b) satisfying the convergence of evolution to(violent resistance tough control) Next we will simulateand analyze the evolution results when the initial state is inthe regions III and IV of Figure 2(b) At this time it isassumed that the proportion x that the resident adoptsrational negotiation is 06 and the proportion y that thegovernment adopts compromised acceptance is 08 and theevolution result is shown in Figure 6

It can be seen from Figure 6 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timethat they evolve to a stable state has been gradually reducedand the fluctuation decreases When the reconnectionprobability p of the small-world network is respectively 0204 06 and 08 the network clustering coefficient is re-spectively 0403 0244 0176 and 0152 and the averagepath length is respectively 2056 1948 1898 and 1896 Italso shows that with the increase of reconnection probabilityof the small-world network the clustering coefficient and theaverage path length decrease making the heterogeneityamong subjects more prominent and the interactioncloseness among the subjects increased and it is easier toachieve equilibrium state

433 Scenario ree -e governmentrsquos extra stability ex-penditure ∆S is large and the residentrsquos violent resistancecost ∆L is small

In scenario three the conditionΔSgt (1 minus α)RgtΔRB + (1 minus β)C αRgtΔRA + βCgtΔL issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 10 and the govern-mentrsquos extra stability expenditure ΔS of tough control is 80When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 7

It can be seen from Figure 7 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability thefluctuation that they evolve to a stable state has beengradually reduced When the reconnection probability p ofthe small-world network is respectively 02 04 06 and 08the network clustering coefficient is respectively 04320242 0164 and 0158 and the average path length is re-spectively 2102 1938 1903 and 1897 It also shows thatwith the increase of reconnection probability of the small-world network the clustering coefficient and the averagepath length decrease Similar to scenario one and two the

(a) (b)

(c) (d)

Figure 5 -e evolutionary result when the reconnection probability p takes different values in scenario two (the initial state is located inregion I and II) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d)the evolutionary result when p 08

12 Complexity

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

(a) (b)

(c) (d)

Figure 6-e evolutionary result when the reconnection probability p of the small-world network takes different values under scenario two(the initial state is located in region III and IV) (a) the evolutionary result when p 02 (b) the evolutionary result when p 04 (c) theevolutionary result when p 06 (d) the evolutionary result when p 08

(a) (b)

(c) (d)

Figure 7 -e evolutionary result when the reconnection probability p takes different values in scenario three (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

Complexity 13

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

decrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

434 Scenario Four -e governmentrsquos extra stability ex-penditure ∆S is small and the residentrsquos violent resistancecost ∆L is large

In scenario four the condition(1 minus α)RgtΔRB + (1 minus β)CgtΔS ΔLgt αRgtΔRA + βC issatisfied and the assumed parameter is set as follows theresidentrsquos violent resistance cost ΔL is 40 and the govern-mentrsquos extra stability expenditure ∆S of tough control is 20When the reconnection probability p of the small-worldnetwork takes different values the evolutionary results of thegame between the resident and the government are shown inFigure 8

It can be seen from Figure 8 that when the reconnectionprobability p of the small-world network takes differentvalues the evolutionary game trends of the resident and thegovernment are basically the same and the final equilibriumtends to (rational negotiation compromised acceptance)but with the increase of reconnection probability the timeand fluctuation that they evolve to a stable state have beengradually reduced When p is 08 the fluctuation of theproportion that the government chooses compromised ac-ceptance strategy is extremely small and basically reaches a

relatively stable state When the reconnection probability p

is respectively 02 04 06 and 08 the network clusteringcoefficient is respectively 0422 023 0177 and 0157 andthe average path length is respectively 2077 1932 1907and 1893 It also shows that with the increase of recon-nection probability of the small-world network the clus-tering coefficient and the average path length decrease -edecrease of clustering coefficient and the average path lengthmakes the heterogeneity among subjects more prominent-e interaction closeness among the subjects gets increasedand it is easier to achieve equilibrium state

5 Conclusions

-is paper constructs an evolutionary game model betweenthe government and the resident which are the two keygame subjects in large-scale engineering projects and an-alyzes game equilibrium results and their adjustment pro-cesses of the governmentrsquos extra stability expenditure andthe residentrsquos violent resistance cost in different situationsBased on the complex network formed by the interactionamong the subjects the small-world network is used as thecomplex network topology and the NetLogo simulationplatform is used to analyze the stakeholder conflict ampli-fication of the large-scale engineering projects on the small-world network -e result shows as follows

(1) In scenario one scenario two here it specificallyrefers to the initial state which is located in regions

(a) (b)

(c) (d)

Figure 8 -e evolutionary result when the reconnection probability p takes different values in scenario four (a) the evolutionary resultwhen p 02 (b) the evolutionary result when p 04 (c) the evolutionary result when p 06 (d) the evolutionary result when p 08

14 Complexity

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

III and IV scenario three and scenario four we findthat both the final evolution results of the residentand the government are (rational negotiationcompromised acceptance) Compared with scenariotwo and scenario three the resident in scenario oneand scenario four has a relatively stable evolutionarystate for a relatively short period of time and thefluctuation after getting relatively stable state is alsosmall the possible reason is that the residentrsquos violentresistance cost ΔL is large and the cost that theresident chooses violent resistance strategy to ex-press their interest appeal is too high In most casesthey will abandon violent resistance strategy andadopt rational negotiation strategy On the otherhand compared with scenario one and scenariothree the time that the government evolves to theequilibrium state in scenario two and scenario four islonger and fluctuates more -e possible reason forthis situation is that when the governmentrsquos addi-tional stability expenditure ΔS is small the gov-ernment is prone to adopt extremely tough controlstrategy for its own interests to cope with the resi-dentrsquos interest appeal resulting in difficulties inachieving equilibrium state or large fluctuations aftergetting the relatively equilibrium state -erefore inorder to control the amplification of conflicts be-tween the resident and the government effectivemeasures should be taken to increase the residentrsquosviolent resistance that is to increase the intensity ofpunishment for violent resistance On the otherhand it should be emphasized that the governmentshould not only consider the additional stabilityexpenditure but also various social impacts in manyaspects when choosing tough control strategy Wecannot easily choose tough control strategy becauseof small stability expenditure

(2) It can be further seen from the influence of differentnetwork characteristics on the evolution results thatas the probability of network reconnection increasesthe time that evolving to the relative equilibriumstate decreases accordingly -is is because on thesmall-world network the average path length andthe clustering coefficient are correspondingly re-duced due to the increase of the probability ofnetwork reconnection On the one hand the smallerthe average path length the smaller the scale of theconflict network between the resident and thegovernment the stronger the intersubjectsrsquo closenessis and the faster the evolution process of the conflictOn the other hand the reduction of the clusteringcoefficient makes the conflict network between thegovernment and the resident presents a decentral-ized state and the heterogeneity of the network ismore obvious Individuals with large nodes havegreater influence easier to influence neighboringnodes to accept their strategies and form a herdeffect so that the time that all individuals evolve to arelatively equilibrium state is reduced On the

realistic network some individuals who are at thecore status and have more social relationships havegreater influence on other individuals and the choiceof their strategies will become the reference for otherindividuals -erefore for these special individualscommunication and guidance should be strength-ened to minimize the choice of violent resistancestrategies and to play a correct guiding role for otherindividuals on the network leading other individualsto choose reasonable manners of interest appeal

-ere are two limitations in this paper Firstly this papercombines the actual situation and literature of the con-struction of large-scale engineering projects in Chinasimplifying the multisubject conflicts into the conflict be-tween the government and the resident only between whichthe evolutionary game model is build Secondly in thesimulation study of the large-scale engineering projectconflicts on the small-world network the hypothetical as-signments of the relevant parameters such as network scalethe residentrsquos violent resistance cost and the governmentrsquosextra stability expenditure are still not quite accurate al-though they are determined on the basis of a large number ofreadings and interviews with relevant experts Further re-search in this paper should focus on the following two as-pects firstly further analyzing the relationships amongrelevant stakeholders rather than the government and theresident considering conflicts among more stakeholdersand improving the existing evolutionary game model andsecondly enriching the collection of relevant data and socialsurveys making the selection of relevant parameters insimulation research more scientific and reasonable

Data Availability

-e data used to support the finding of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (nos 71603070 and 71573072) theChina Postdoctoral Science Foundation (no 2019M661719)the Ministry of Education of Humanities and Social Scienceof China (no 17YJC630144) and the Fundamental ResearchFunds for the Central Universities (no 2019B34314)

References

[1] J Miao D Huang and Z He ldquoSocial risk assessment andmanagement for major construction projects in China basedon fuzzy integrated analysisrdquo Complexity vol 2019 Article ID2452895 17 pages 2019

[2] B Flyvbjerg ldquoWhat you should know about megaprojects andwhy an overviewrdquo Project Management Journal vol 45 no 2pp 6ndash19 2014

Complexity 15

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

[3] G Jia F Yang G Wang B Hong and R You ldquoA study ofmega project from a perspective of social conflict theoryrdquoInternational Journal of Project Management vol 29 no 7pp 817ndash827 2011

[4] E Cuppen M G C Bosch-Rekveldt E Pikaar andD C Mehos ldquoStakeholder engagement in large-scale energyinfrastructure projects revealing perspectives using Qmethodologyrdquo International Journal of Project Managementvol 34 no 7 pp 1347ndash1359 2016

[5] Z-z Liu Z-w Zhu H-j Wang and J Huang ldquoHandlingsocial risks in government-driven mega project an empiricalcase study from West Chinardquo International Journal of ProjectManagement vol 34 no 2 pp 202ndash218 2016

[6] Y Hu A P Chan Y Le and R Z Jin ldquoFrom constructionmegaproject management to complex project managementbibliographic analysisrdquo Journal of Management in Engineer-ing vol 31 no 4 Article ID 04014052 2013

[7] T Yu G Q Shen Q Shi X Lai C Z Li and K XuldquoManaging social risks at the housing demolition stage ofurban redevelopment projects a stakeholder-oriented studyusing social network analysisrdquo International Journal of ProjectManagement vol 35 no 6 pp 925ndash941 2017

[8] K Y Mok G Q Shen R J Yang and C Z Li ldquoInvestigatingkey challenges in major public engineering projects by anetwork-theory based analysis of stakeholder concerns a casestudyrdquo International Journal of Project Management vol 35no 1 pp 78ndash94 2017

[9] Z He D Huang C Zhang and J Fang ldquoToward a stake-holder perspective on social stability risk of large hydraulicengineering projects in China a social network analysisrdquoSustainability vol 10 no 4 Article ID 1223 2018

[10] S-u-R Toor and S O Ogunlana ldquoBeyond the rsquoiron trianglersquostakeholder perception of key performance indicators (KPIs)for large-scale public sector development projectsrdquo Interna-tional Journal of Project Management vol 28 no 3pp 228ndash236 2010

[11] R Takim ldquo-e management of stakeholdersrsquo needs and ex-pectations in the development of construction project inMalaysiardquoModern Applied Science vol 3 no 5 pp 167ndash1752009

[12] K Callan C Sieimieniuch and M Sinclair ldquoA case studyexample of the role matrix techniquerdquo International Journalof Project Management vol 24 no 6 pp 506ndash515 2006

[13] X Lin C M F Ho and G Q P Shen ldquoWho should take theresponsibility Stakeholdersrsquo power over social responsibilityissues in construction projectsrdquo Journal of Cleaner Produc-tion vol 154 pp 318ndash329 2017

[14] J K Pinto and P W Morris e Wiley Guide to ManagingProjects Wiley Hoboken NJ USA 2004

[15] M Leung J Yu and Q Liang ldquoAnalysis of the relationshipsbetween value management techniques conflict managementand workshop satisfaction of construction participantsrdquoJournal of Management in Engineering vol 30 no 3 ArticleID 04014004 2014

[16] J L Brockman ldquoInterpersonal conflict in construction costcause and consequencerdquo Journal of Construction Engineeringand Management vol 140 no 2 Article ID 04013050 2014

[17] R Awwad B Barakat and C Menassa ldquoUnderstandingdispute resolution in theMiddle East region from perspectivesof different stakeholdersrdquo Journal of Management in Engi-neering vol 32 no 6 Article ID 05016019 2016

[18] C Lee J W Won W Jang W Jung S H Han andY H Kwak ldquoSocial conflict management framework forproject viability case studies from Korean megaprojectsrdquo

International Journal of Project Management vol 35 no 8pp 1683ndash1696 2017

[19] Y Sun ldquoAnalysis on major social problems in the three gorgesreservoir area in post-migration period their causes and thesuggestions for their solutionrdquo China Soft Science Magazinevol 2011 no 6 pp 24ndash33 2011 in Chinese

[20] S C Wright D M Taylor and F M MoghaddamldquoResponding to membership in a disadvantaged group fromacceptance to collective protestrdquo Journal of Personality andSocial Psychology vol 58 no 6 pp 994ndash1003 1990

[21] M Van Zomeren T Postmes and R Spears ldquoToward anintegrative social identity model of collective action aquantitative research synthesis of three socio-psychologicalperspectivesrdquo Psychological Bulletin vol 134 no 4pp 504ndash535 2008

[22] M M M Teo and M Loosemore ldquo-e role of core protestgroup members in sustaining protest against controversialconstruction and engineering projectsrdquo Habitat Interna-tional vol 44 pp 41ndash49 2014

[23] Z Liu L Liao and CMei ldquoNot-in-my-backyard but letrsquos talkexplaining public opposition to facility siting in urban ChinardquoLand Use Policy vol 77 pp 471ndash478 2018

[24] P Enevoldsen and B K Sovacool ldquoExamining the socialacceptance of wind energy practical guidelines for onshorewind project development in Francerdquo Renewable and Sus-tainable Energy Reviews vol 53 pp 178ndash184 2016

[25] M Wang and H Gong ldquoNot-in-My-Backyard legislationrequirements and economic analysis for developing under-ground wastewater treatment plant in Chinardquo InternationalJournal of Environmental Research and Public Health vol 15no 11 Article ID 2339 2018

[26] K Burningham J Barnett and G Walker ldquoAn array ofdeficits unpacking NIMBY discourses in wind energy de-velopersrsquo conceptualizations of their local opponentsrdquo Societyamp Natural Resources vol 28 no 3 pp 246ndash260 2014

[27] B Liu Y Li B Xue Q Li P X W Zou and L Li ldquoWhy doindividuals engage in collective actions against major con-struction projects -An empirical analysis based on Chinesedatardquo International Journal of Project Management vol 36no 4 pp 612ndash626 2018

[28] W Wang ldquoRisk amplification collective action and policygame a descriptive analysis about environmental groupsstruggle violencerdquo Journal of Public Management vol 12no 1 pp 127ndash136 2015 in Chinese

[29] D Liu C Han and L Yin ldquoMulti-scenario evolutionary gameanalysis of evolutionary mechanism in urban demolition massincidentrdquo Operations Research and Management Sciencevol 25 no 1 pp 76ndash84 2016 in Chinese

[30] S Zhao Y Zhou and Y Cai ldquoInvestigation on process andsolution of environmental group events from NIMBY conflictperspectiverdquo China Population Resources and Environmentvol 27 no 6 pp 171ndash176 2017 in Chinese

[31] O Kaplinski and J Tamosaitiene ldquoGame theory applicationsin construction engineering and managementrdquo Technologicaland Economic Development of Economy vol 16 no 2pp 348ndash363 2010

[32] C Li X Li and Y Wang ldquoEvolutionary game analysis of thesupervision behavior for public-private partnership projectswith public participationrdquo Mathematical Problems in Engi-neering vol 2016 Article ID 1760837 8 pages 2016

[33] C Cohen D Pearlmutter and M Schwartz ldquoA gametheory-based assessment of the implementation of greenbuilding in Israelrdquo Building and Environment vol 125pp 122ndash128 2017

16 Complexity

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17

[34] A S Barough M V Shoubi and M J E Skardi ldquoApplicationof game theory approach in solving the construction projectconflictsrdquo Procedia-Social and Behavioral Sciences vol 58pp 1586ndash1593 2012

[35] C-C Kang T-S Lee and S-C Huang ldquoRoyalty bargainingin Public-Private Partnership projects insights from a the-oretic three-stage game auction modelrdquo Transportation Re-search Part E Logistics and Transportation Review vol 59pp 1ndash14 2013

[36] G Wu H Wang and R Chang ldquoA decision model assessingthe owner and contractorrsquos conflict behaviors in constructionprojectsrdquo Advances in Civil Engineering vol 2018 Article ID1347914 11 pages 2018

[37] C He G Jia and J Sun ldquoGovernance strategy analysis ofproject safety behavior from the perspective of three-partygame theoryrdquo Soft Science vol 33 no 1 pp 87ndash90 2019 inChinese

[38] M Cheng Y Liu and H Wang ldquoAn evolutionary gameanalysis on the PPP projects of NIMBY facility based onsystem dynamicsrdquo Operations Research and ManagementScience vol 28 no 10 pp 40ndash49 2019 in Chinese

[39] S He G Liang and J Meng ldquoMulti-subjects benefit game andbehavior evolution mechanism of major engineering based onprospect theoryrdquo Science and Technology Management Re-search vol 40 no 5 pp 207ndash214 2020 in Chinese

[40] D J Watts and S H Strogatz ldquoCollective dynamics of rsquosmall-worldrsquo networksrdquo Nature vol 393 no 6684 pp 440ndash4421998

[41] A-L Barabasi and R Albert ldquoEmergence of scaling in ran-dom networksrdquo Science vol 286 no 5439 pp 509ndash512 1999

[42] M A Nowak and R MMay ldquoEvolutionary games and spatialchaosrdquo Nature vol 359 no 6398 pp 826ndash829 1992

[43] C Hauert andM Doebeli ldquoSpatial structure often inhibits theevolution of cooperation in the snowdrift gamerdquo Naturevol 428 no 6983 pp 643ndash646 2004

[44] J Vukov G Szabo and A Szolnoki ldquoEvolutionary prisonerrsquosdilemma game on Newman-Watts networksrdquo Physical ReviewE vol 77 no 2 Article ID 026109 2008

[45] G Szabo L Varga and M Szabo ldquoAnisotropic invasion andits consequences in two-strategy evolutionary games on asquare latticerdquo Physical Review E vol 94 no 5 Article ID052314 2016

[46] R Fan L Dong W Yang and J Sun ldquoStudy on the optimalsupervision strategy of government low-carbon subsidy andthe corresponding efficiency and stability in the small-worldnetwork contextrdquo Journal of Cleaner Production vol 168pp 536ndash550 2017

[47] D Liu and W Wang ldquoCo-evolutionary mechanism of socialnetwork structure and strategy in mass emergency withmaintain legal rightsrdquo Chinese Journal of Management Sci-ence vol 20 no 3 pp 185ndash192 2012 in Chinese

[48] Y Bian J Li and L Xu ldquoSimulation and evolution model offeeding behavior in stock market based on the strategy ofcoordination game in networkrdquo Chinese Journal of Man-agement Science vol 25 no 3 pp 20ndash29 2017 in Chinese

[49] Y Fang W Wei S Mei L Chen X Zhang and S HuangldquoPromoting electric vehicle charging infrastructure consid-ering policy incentives and user preferences an evolutionarygame model in a small-world networkrdquo Journal of CleanerProduction vol 258 2020

[50] X Luo L Hu and D Liu ldquoSocial stability risk assessment ofmajor engineering project under conditions of black-boxoperation and information disclosure dynamic game analysis

based on hierarchical bayesian networkrdquo Technology Eco-nomics vol 37 no 10 pp 117ndash130 2018 in Chinese

[51] M Song and D Liu ldquoStochastic evolutionary game model forresolution mechanism of mass eventsrdquo Chinese Journal ofManagement Science vol 28 no 4 pp 142ndash152 2020 inChinese

Complexity 17