research article study on evolutionary path of university

Research ArticleStudy on Evolutionary Path of University Students’Entrepreneurship Training

Daojian Yang and Xicang Zhao

School of Management, Jiangsu University, Zhenjiang, Jiangsu Province 212013, China

Correspondence should be addressed to Daojian Yang; [email protected]

Received 15 February 2014; Accepted 21 April 2014; Published 22 May 2014

Academic Editor: Jianguo Du

Copyright © 2014 D. Yang and X. Zhao.This is an open access article distributed under the Creative CommonsAttribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Aiming at studying the evolution pattern of cultivating the ability of university students’ entrepreneurship, this paper establishedthe payoffmatrix between the university and students agent with the evolutionary economics method.The analysis of the evolutionof the communication process model reveals how the choice strategy of individuals influences that of groups. Numerical simulationalso demonstrates the influences of different values of decision-making parameters and the change of initial conditions on the resultof evolution. It is found that the evolution path system of university students’ entrepreneurial ability has two kinds of modes: oneis the ideal state; and the other one is the bad “lock” state. By adjusting parameters, we can jump out of the bad “lock” state, thusoptimizing cultivation path.

1. Introduction

It has become a necessity for universities to cultivate students’entrepreneurial ability to adapt to the economic transfor-mation and upgrading, as well as to the construction anddevelopment of entrepreneurial economy. It is also importantto improve the education system in colleges and universities,strengthening the innovation training of entrepreneurialtalent. With this progress, promoting the overall develop-ment of people and cultivating entrepreneurial qualities ofa new generation can be achieved. Gorman et al. analyzedthe literature about entrepreneurship education in the 10years from 1985 to 1994 and point out that the cultivationof entrepreneurship for college students plays the func-tion of entrepreneurship preparation and can enhance theindividual’s self-efficacy. During this process, universitiesshould focus on the improvement of students’ entrepreneurialqualities and skills [1]. Fayolle discussed the concept ofentrepreneurial education and its theoretical framework, thepioneering education paradigm, entrepreneurship educationmode, education assessment, target, function, interdisci-plinary approach, and so forth, putting forward the innova-tive teaching mode to enhance the level of entrepreneurship[2]. O’Connor believes that entrepreneurial talent training isan effective mean of promoting economic development [3].

Research on college students’ entrepreneurial abilitytraining was mainly concentrated on the content ofentrepreneurship education and entrepreneurial ability train-ing mode. For entrepreneurial education content, Harrisonand Leitch’s research “Entrepreneurship and Leadership: edu-cation and enlightenment” has paved the way for the researchon entrepreneurship education content [4]. Jack and Ander-son find that entrepreneurship education activity involves theareas of science and art, which need to research entrepreneur-ship education theory to connect the gap between scienceand art [5]. Fiet studied the theoretical dimension of teachingentrepreneurship, emphasizing that more attention shouldbe paid to the teaching of entrepreneurship theory [6].Kent and Anderson argue that the spirit of cooperation,social ability, and pioneering consciousness should be putinto the training content of entrepreneurship education [7];some other scholars suggest “business failure” as one part ofentrepreneurial education [8]. Sudharson et al. tried to wakeup all engineering students’ entrepreneurial ideas and inspiretheir entrepreneurial spirit, so in the original curriculumsystem, they design to added a few additional modulesabout entrepreneurship [9]. For entrepreneurial abilitytraining mode, Johannisson et al. make an analysis of kolb’slearning mode. Through the test of entrepreneurial action,they found that different groups (engineering students,

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 535137, 11 pageshttp://dx.doi.org/10.1155/2014/535137

2 Mathematical Problems in Engineering

Table 1: Payoff matrix of universities and students’ strategy.

StudentsParticipation 𝑁

𝑌No participation 𝑁

𝑁

UniversitiesPositive training𝑀

𝑌𝛼(𝛾𝑆1− 1)𝐶

𝑆− 𝐶𝐶, (𝛾𝑆1− 1)𝐶

𝑆−𝐶𝐶, (𝛾𝑆2− 1)𝐶

𝑆

Negative training𝑀𝑁

𝛼 (𝛾𝑆3− 1)𝐶

𝑆, (𝛾𝑆3− 1)𝐶

𝑆0, (𝛾𝑆2− 1)𝐶

𝑆

business school students, and the business operators) havedifferent study effects [10]. Fiet explored the teachingdimension of entrepreneurship theory, finding that thereexist some challenges for the research and education ofentrepreneurship. When entrepreneurship teaching becomespredictable, teaching cannot achieve good results. He holdsthat entrepreneurship education should be based on the the-ory of entrepreneurship [6]. Above all, the existing studies aremainly carried out from the perspective of education part—schools—to cultivate the ability of entrepreneurship, but theyignore the entrepreneurial ability training process, which isthe mutual process of university and college students.

Evolutionary game theory combines the game theorywith dynamic evolution process. It is the result of biologicalevolutionary theory. The analysis of the system of socialhabits, specification, or spontaneous formation and influencefactors has made remarkable achievements. In fact, due tothe insufficient understanding of entrepreneurial ability, toomuch attention has been focused on the theory, less oncultivating the ability of entrepreneurship; thus, problemsexist. In this case, this paper is intended to discuss how tomake both universities and students evolve in an expectedway (inspiring and guiding students’ entrepreneurial ability)so as to improve the training effectiveness of students’entrepreneurial ability.

2. Model Building

In constructing an evolutionary game model, we must makesome basic assumptions of behavior interaction betweenuniversity and college students, up to the present statusof the management of universities. The two sides are theuniversity and students, respectively, with both sides havinglimited rationality. The group-colleges and universities havetwo strategies: one is to actively develop the students’ abilityof entrepreneurship through various channels, hereinafterreferred to as “positive training,” remembered as 𝑀

𝑌and

the other strategy is negative cultivation of college students’entrepreneurial ability, which means universities do not evendo anything, which is referred to as “negative training,”remembered as 𝑀

𝑁. Strategy community of university is

set as 𝑆𝐶{positive training, 𝑀

𝑌; negative training, 𝑀

𝑁}.

The group-students also have two strategies: one is activelyparticipating in activities to develop their entrepreneurialskills, hereinafter referred to as “participation,” rememberedas 𝑁𝑌, while the second strategy is not involved in their

activities that develop their entrepreneurial skills, hereinafterreferred to as “no participation,” noted as𝑁

𝑁. The strategy of

university student group is set as 𝑆𝑆{participation, 𝑁

𝑌and

no participation,𝑁𝑁}.

If universities actively cultivate their students’entrepreneurial ability, they will improve the system ofentrepreneurship education management and entrepreneur-ship education system and create entrepreneurship trainingbase and so on. The cost of these activities is set as 𝐶

𝐶.

If students are actively involved in developing theirentrepreneurial ability, they need to spend the costs of timeand energy, set as 𝐶

𝑆.

When universities are active in entrepreneurial abilitytraining and students are also active in developing theirbusiness ability, students will increase their human capitalvalue, and their costs will have higher returns 𝛾

𝑆1, 𝛾𝑆1

≥ 1.At this point, the net income for the students is (𝛾

𝑆1− 1)𝐶

𝑆.

The net income of colleges and universities is 𝛼(𝛾𝑆1− 1)𝐶

𝑆−

𝐶𝐶, where 𝛼 is the reputation and alumni support through

cultivating high level students for colleges and universities,and 0 ≤ 𝛼 ≤ 1. If students do not participate in developingthe ability of business, they can spare the time and energy inother activities, so at this time, the investment rate of returnis 𝛾𝑆2, and 𝛾

𝑆2≤ 𝛾𝑆1. At this point, the net income for the

students is (𝛾𝑆2

− 1)𝐶𝑆and the net income of universities is

−𝐶𝐶.When universities are negative in cultivating the students’

entrepreneurial ability, students can promote entrepreneur-ship ability through self-study or internship. Without thehelp, support, and guidance of universities, the rate of returnon its investment is lower, set as 𝛾

𝑆3, 𝛾𝑆3

≤ 𝛾𝑆2. At this point,

the net income for the students is (𝛾𝑆3

− 1)𝐶𝑆and the net

income of universities is 𝛼(𝛾𝑆3− 1)𝐶

𝑆. If students themselves

do not actively promote entrepreneurship ability but spendthe time and energy in other activities, the net income forthe students would be (𝛾

𝑆2− 1)𝐶

𝑆, and the net income of

universities is 0.Based on the above assumptions, we constructed the

strategy payoff matrix between the universities and students,as shown in Table 1.

3. The Evolution of the Model andIts Equilibrium Analysis

3.1. The Evolution of the Model. Assume that, in the initialstate, the proportion of universities choosing𝑀

𝑌is𝑝 and that

the proportion of universities choosing strategy𝑀𝑁is 1 − 𝑝;

the proportion of students choosing strategy𝑁𝑌is 𝑞; then, the

proportion of students choosing𝑁𝑁is 1−𝑞. Herewe calculate

the corresponding expected revenue and average income.

Mathematical Problems in Engineering 3

Table 2: Local stability analysis results.

Equilibrium point Det𝐽 Tr Result𝑝 = 0, 𝑞 = 0 −𝐶

𝐶(𝛾𝑆3− 𝛾𝑆2)𝐶𝑆

+ −𝐶𝐶+ (𝛾𝑆3− 𝛾𝑆2)𝐶𝑆

− ESS𝑝 = 0, 𝑞 = 1 − [𝛼(𝛾

𝑆1− 𝛾𝑆3)𝐶𝑆− 𝐶𝐶] (𝛾𝑆3− 𝛾𝑆2)𝐶𝑆

+ 𝛼(𝛾𝑆1− 𝛾𝑆3)𝐶𝑆− 𝐶𝐶− (𝛾𝑆3− 𝛾𝑆2)𝐶𝑆

+ Not stable𝑝 = 1, 𝑞 = 0 𝐶

𝐶(𝛾𝑆1− 𝛾𝑆2)𝐶𝑆

+ 𝐶𝐶+ (𝛾𝑆1− 𝛾𝑆2)𝐶𝑆

+ Not stable𝑝 = 1, 𝑞 = 1 [𝛼(𝛾

𝑆1− 𝛾𝑆3)𝐶𝑆− 𝐶𝐶] (𝛾𝑆1− 𝛾𝑆2)𝐶𝑆

+ − [𝛼(𝛾𝑆1− 𝛾𝑆3)𝐶𝑆− 𝐶𝐶] − (𝛾

𝑆1− 𝛾𝑆2)𝐶𝑆

− ESS𝑝 = 𝑝

∗, 𝑞 = 𝑞∗

−𝑝∗𝑞∗(1 − 𝑝

∗)(1 − 𝑞

∗)𝛼(𝛾𝑆1− 𝛾𝑆3)2𝐶𝑆

2− 0 saddle point

𝑈1is the expected return of the selection of universities to

𝑀𝑌strategy; 𝑈

2is the expected return of universities choos-

ing 𝑀𝑁

strategy; 𝑈 is the average income of universities.Consider the following:

𝑈1= 𝑞 [𝛼 (𝛾

𝑆1− 1)𝐶

𝑆− 𝐶𝐶] + (1 − 𝑞) (−𝐶

𝐶)

= 𝑞𝛼 (𝛾𝑆1− 1)𝐶

𝑆− 𝐶𝐶,

𝑈2= 𝑞𝛼 (𝛾

𝑆3− 1)𝐶

𝑆,

𝑈 = 𝑝𝑈1+ (1 − 𝑝)𝑈

2.

(1)

Similarly, 𝑉1is the expected return of students choosing

𝑁𝑌strategy; 𝑉

2is the expected return for students choosing

𝑁𝑁strategy; 𝑉 is the average income for students. Consider

the following:

𝑉1= 𝑝 (𝛾

𝑆1− 1)𝐶

𝑆+ (1 − 𝑝) (𝛾

𝑆3− 1)𝐶

𝑆

= 𝑝 (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆+ (𝛾𝑆3− 1)𝐶

𝑆,

𝑉2= (𝛾𝑆2− 1)𝐶

𝑆,

𝑉 = 𝑞𝑉1+ (1 − 𝑞)𝑉

2.

(2)

According to the Malthusian dynamic equation, thegrowth rate of the strategy is equal to its correspondingfitness [11, 12]; hence, we can draw dynamics equations ofthe interaction strategy that evolved over time betweenuniversities and students:

𝐹 (𝑝) =𝑑𝑝

𝑑𝑡= 𝑝 (𝑈

1− 𝑈)

= 𝑝 (1 − 𝑝) [𝑞𝛼 (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆− 𝐶𝐶] ,

𝐹 (𝑞) =𝑑𝑞

𝑑𝑡= 𝑞 (𝑉 − 𝑉)

= 𝑞 (1 − 𝑞) [𝑝 (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆+ (𝛾𝑆3− 𝛾𝑆2) 𝐶𝑆] .

(3)

Through (3), we can study the evolution of the interactionbehavior between universities and students. Mark the Jaco-bian matrix of (3) as 𝐽 which is expressed by

𝐽 =[[[

[

𝑑𝐹 (𝑝)

𝑑𝑝

𝑑𝐹 (𝑝)

𝑑𝑞

𝑑𝐹 (𝑞)

𝑑𝑝

𝑑𝐹 (𝑞)

𝑑𝑞

]]]

]

= [(1 − 2𝑝) [𝑞𝛼 (𝛾

𝑆1− 𝛾𝑆3) 𝐶𝑆− 𝐶𝐶] 𝑝 (1 − 𝑝) 𝛼 (𝛾

𝑆1− 𝛾𝑆3) 𝐶𝑆

𝑞 (1 − 𝑞) (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆

(1 − 2𝑞) [𝑝 (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆+ (𝛾𝑆3− 𝛾𝑆2) 𝐶𝑆]] .

(4)

The determinant of the Jacobian matrix is marked as Det 𝐽,and the trace of the Jacobianmatrix ismarked as Tr. Consider

Det 𝐽 = (1 − 2𝑝) (1 − 2𝑞) [𝑞𝛼 (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆− 𝐶𝐶]

× [𝑝 (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆+ (𝛾𝑆3− 𝛾𝑆2) 𝐶𝑆]

− 𝑝𝑞 (1 − 𝑝) (1 − 𝑞) 𝛼(𝛾𝑆1− 𝛾𝑆3)2𝐶𝑆

2,

(5)

Tr = (1 − 2𝑝) [𝑞𝛼 (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆− 𝐶𝐶]

+ (1 − 2𝑞) [𝑝 (𝛾𝑆1− 𝛾𝑆3) 𝐶𝑆+ (𝛾𝑆3− 𝛾𝑆2) 𝐶𝑆] .

(6)

3.2. Equilibrium and Its Stability Analysis. Since 𝑝 and 𝑞,respectively, represent the proportion of universities’ andstudents’ choices of the strategies above, it is drawn that 0 ≤

𝑝 ≤ 1, 0 ≤ 𝑞 ≤ 1. On a plane 𝑀∗= {(𝑝, 𝑞) | 0 ≤ 𝑝, 𝑞 ≤ 1}, the

system has 5 equilibrium points: (0, 0), (0, 1), (1, 0), (1, 1),and (𝑝

∗, 𝑞∗). Among them, 𝑝∗ = (𝛾

𝑆2− 𝛾𝑆3)/(𝛾𝑆1− 𝛾𝑆3) and

𝑞∗= 𝐶𝐶/𝛼(𝛾𝑆1−𝛾𝑆3)𝐶𝑆. According to the Jacobianmatrix, we

can have the local buckling analysis results in Table 2.According to Table 2, (𝑝∗, 𝑞∗) is the saddle point, and

(0, 1) and (1, 0) are the instability points. (0, 0) and (1, 1)

are the evolutionary stable strategy, corresponding to themodes (𝑀

𝑁, 𝑁𝑁) and (𝑀

𝑌, 𝑁𝑌). Here, (𝑀

𝑁, 𝑁𝑁)means the

university and students both choose negative action, which


q

o p

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)

Figure 1: Systematic dynamic evolution.

is badly locked; (𝑀𝑌, 𝑁𝑌)means the university and students

choose positive action, which is an ideal condition. Figure 1shows the strategy communication process of university andstudents groups.

4. The Influence of Parameter Change onthe Convergence System

(1) The impact of 𝐶𝐶, 𝛼 and 𝐶

𝑆on the system convergence

In the saddle point, 𝜕𝑝/𝜕𝐶𝐶

= 0, 𝜕𝑞/𝜕𝐶𝐶

= 1/𝛼(𝛾𝑆1

−

𝛾𝑆3)𝐶𝑆

> 0. When other parameters remain constant, 𝐶𝐶

increases, 𝛼 or 𝐶𝑆decreases, and saddle point goes upward

vertically. The probability of converging to mode (𝑀𝑁, 𝑁𝑁)

increases, and the probability of convergence to (𝑀𝑌, 𝑁𝑌)

decreases; on the contrary, the probability of converging tomode (𝑀

𝑁, 𝑁𝑁) is reduced, and the probability of conver-

gence to (𝑀𝑌, 𝑁𝑌) increases, which is shown in Figure 2.

(2) The impact of 𝛾𝑆1on the system convergence

In the saddle point, 𝜕𝑝/𝜕𝛾𝑆1

= −(𝛾𝑆2− 𝛾𝑆3)/(𝛾𝑆1− 𝛾𝑆2)2<

0, 𝜕𝑞/𝜕𝛾𝑆1

= −𝐶𝐶/𝛼(𝛾𝑆1− 𝛾𝑆3)2𝐶𝑆

< 0. When the otherparameters remain constant, 𝛾

𝑆1increases, and saddle point

moves to the lower left corner, so the probability of con-verging to mode (𝑀

𝑁, 𝑁𝑁) is reduced, and the probability

of convergence in (𝑀𝑌, 𝑁𝑌) increases; on the contrary, the

probability of converging to mode (𝑀𝑁, 𝑁𝑁) increases, and

the probability of convergence in (𝑀𝑌, 𝑁𝑌) is reduced, which

is shown in Figure 3.(3) The impact of 𝛾

𝑆2on the system convergence


= 1/(𝛾𝑆1−𝛾𝑆2) > 0, 𝜕𝑞/𝜕𝛾

𝑆2=

0. When the other parameters remain constant, 𝛾𝑆2increases,

and saddle point moves to the right corner, so the probabilityof converging to mode (𝑀

𝑁, 𝑁𝑁) increases, and the proba-

bility of convergence in (𝑀𝑌, 𝑁𝑌) decreases; on the contrary,

the probability of converging to mode (𝑀𝑁, 𝑁𝑁) reduces,

and the probability of convergence in (𝑀𝑌, 𝑁𝑌) increases,

which is shown in Figure 4.

(4) The impact of 𝛾𝑆3on the system convergence


= −1/(𝛾𝑆1

− 𝛾𝑆2) <

0, 𝜕𝑞/𝜕𝛾𝑆3

= 𝐶𝐶/𝛼(𝛾𝑆3

− 𝛾𝑆1)2𝐶𝑆

> 0. When the otherparameters remain constant, 𝛾

𝑆3increases, and the saddle

point moves to the top left; on the contrary, the saddle pointmoves to the lower right, as is shown in Figure 5. The impactof 𝛾𝑆3

on the results of the convergence system is not clear,which needs further numerical analysis.

5. The Result Analysis ofNumerical Experiments

In behavior strategy communication system between uni-versity and students, some parameters are involved: theproportion of initial population 𝑝 and 𝑞, the respective costof college and students 𝐶

𝐶and 𝐶

𝑆, the rate of reward 𝛾

𝑆1, 𝛾𝑆2,

and 𝛾𝑆3

of students under different situations, and rewardcoefficient 𝛼 of universities. These parameters will influencethe earnings of university and students, which will furtherinfluence the evolution of the system.

(1)The impact of the changes of 𝑝0and 𝑞0on the result of

system evolutionAccording to the numerical experiment shown in

Figure 6, 𝑝0and 𝑞

0, respectively, represent the proportion

of the initial population that university chooses 𝑀𝑌and

students who choose𝑁𝑌. Parameter values are 𝐶

𝐶= 1, 𝐶

𝑆=

10, 𝛼 = 0.2, 𝛾𝑆1

= 2, 𝛾𝑆2

= 1.5, and 𝛾𝑆3

= 1.2. It can be seenfrom Figure 6 the dependence of the path when universityand students are in the process of behavior strategy interac-tion. With different initial ratio the convergence curves donot overlap before reaching their equilibrium. Convergencespeed is influenced not only by the initial proportion studentschoosing to have entrepreneurial ability training, but also bythe initial proportion that students have related actions toimprove their entrepreneurial abilities at the same time. Thecloser the proportion gets to the equilibrium, the faster theconvergence speed is. As long as the proportion of initial𝑀𝑌strategy use is very low (e.g., 𝑝

0= 0.1), the system will

eventually be locked in a “bad” state; if this proportion isvery high (e.g., 𝑝

0= 0.9), the system can eventually evolve

to the ideal mode (𝑀𝑌, 𝑁𝑌). In general circumstances, as

the proportion of students choosing to have positive actionincreases, it will also help the system evolve toward theideal mode; therefore, universities must first enhance theentrepreneurship education actively, arousing the students’enthusiasm.

(2)The impact of the change of𝐶𝐶on the result of system

evolutionNumerical test results of the impact are shown inFigure 7.

The reason that we set the proportion of students taking partin the entrepreneurship activities as 0.4 is that as the impactof the change of the initial population on the evolution is ana-lyzed above, it is clear that when the initial choice ratio of uni-versities’ cultivating students’ entrepreneurship is high, thesystem will converge to (𝑀

𝑌, 𝑁𝑌) mode; if the initial choice

ratio of universities’ cultivating students’ entrepreneurshipis lower, the system will converge to mode (𝑀

𝑁, 𝑁𝑁). So

𝑞 = 0.4 is a typical situation. At the same time, combining


q

o p

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)

(a) The situation of 𝐶𝐶 increases, 𝛼 or 𝐶𝑆 decreases

q

o p

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)

(b) The situation of 𝐶𝐶 decreases, 𝛼 or 𝐶𝑆 increases

Figure 2: The impact of 𝐶𝐶, 𝛼, 𝐶

𝑆on the system convergence.

q

o p

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)

(a) The situation when 𝛾𝑆1 increases

q

o p

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)

(b) The situation when 𝛾𝑆1 decreases

Figure 3: The impact of 𝛾𝑆1on the system convergence.

the fact that the overall university students are in highenthusiasm but with lower ability in entrepreneurial activities(national college students entrepreneurship research reportshows that 14% of students participated in a training programor entrepreneurship competition and that 48.8% of collegestudents hope to be provided with business related profes-sional training) and choosing 𝑞 = 0.4, which is more inline with the actual situation, other parameter values are asfollows: 𝐶

𝑆= 10, 𝛼 = 0.2, 𝛾

𝑆1= 2, 𝛾

𝑆2= 1.5, and 𝛾

𝑆3= 1.2.

As Figure 7 shows, with the increase of university’straining cost 𝐶

𝐶, the convergence speed of the system slows

down and the time of convergence to equilibrium mode

increases, and the system’s evolutionary direction convertsfrommode (𝑀

𝑌, 𝑁𝑌) to a bad lockmode (𝑀

𝑁, 𝑁𝑁). Univer-

sities’ training cost represents the burden of entrepreneurshiptraining of universities. Under the certain level of total costof entrepreneurship training, universities’ burden should beeased by broadening the financing channels. This can notonly guarantee the training level, but also arouse universities’training enthusiasm.

(3)The impact of the change of 𝐶𝑆on the result of system

evolutionThe impact is shown in Figure 8. The parameter values

are as follows: 𝑞 = 0.4, 𝐶𝐶

= 1, 𝛼 = 0.2, 𝛾𝑆1

=


q

o p

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)


q

o p

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)


Figure 4: The impact of 𝛾𝑆2on the system convergence.

q

op

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)


q

o p

N(0, 1)

M(p∗, q∗)

L(1, 1)

H(1, 0)


Figure 5: The impact of 𝛾𝑆3on system convergence.

2, 𝛾𝑆2

= 1.5, and 𝛾𝑆3

= 1.2. It can be seen fromFigure 8 that with the increase of students’ entrepreneurialactivity costs𝐶

𝑆, system convergence speeds up, and the time

of converging to equilibrium mode reduces. The evolutiondirection of the system will also change from bad lock mode(𝑀𝑁, 𝑁𝑁) to the ideal mode (𝑀

𝑌, 𝑁𝑌). The cost 𝐶

𝑆reflects

the difficulty level of promoting entrepreneurship skills. Wecan see that more college students tend to participate inthe school’s entrepreneurial ability training program, ratherthan to choose self-study to gain their entrepreneurial skills.Therefore, in the process of entrepreneurship education, uni-versities should paymore attention to the core and important

business knowledge, while the simple and easy knowledgecan be learned by students themselves. Universities need todistinguish between the focus of entrepreneurship educationand the investment of education resources.

(4)The impact of the change of 𝛾𝑆1on the result of system

evolutionThe impact is shown in Figure 9, and the parameter value

selections are as follows: 𝑞 = 0.4, 𝐶𝐶

= 1, 𝐶𝑆= 10, 𝛼 =

0.2, 𝛾𝑆2

= 1.5, 𝛾𝑆3

= 1.2.As can be seen from Figure 9, with the increase of the

investment return ratio 𝛾𝑆1of students’ entrepreneurial ability

improvement, the system convergence speeds up, and the


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0 10 20

t

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0 10 20

t

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0 10 20

t

0 10 20

t

q0 = 0.1 q0 = 0.4 q0 = 0.6 q0 = 0.9

Figure 6: Impact of the change of 𝑝0and 𝑞

0on the result of the system evolution.

0 20 40

t

0 20 40

t

0 20 40

t

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

CC = 0.5 CC = 1.0 CC = 1.5

Figure 7: Impact of the changes of 𝐶𝐶on the result of the system evolution.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

0 20 40

t

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0 20 40

t

0 20 40

t

CS = 7 CS = 10 CS = 15

Figure 8: Impact of the changes of 𝐶𝑆on the result of the system evolution.

0 20 40

t

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0 20 40

t

0 20 40

t

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

𝛾S1 = 1.8 𝛾S1 = 2.0 𝛾S1 = 2.5

Figure 9: Impact of the change of 𝛾𝑆1on the result of the system evolution.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0 10 20

t

0 10 20

t

0 10 20

t

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

𝛾S2 = 1.3 𝛾S2 = 1.5 𝛾S2 = 1.8

Figure 10: Impact of the change of 𝛾𝑆2on the result of the system evolution.

evolution direction of the system will be changed from(𝑀𝑁, 𝑁𝑁) into the ideal mode (𝑀

𝑌, 𝑁𝑌). Increasing 𝛾

𝑆1

means that more entrepreneurial investment can lead toability improvement and significant increase of their ownhuman capital value. At the same time universities can alsoget high school reputation. In the condition of a higher 𝛾

𝑆1,

both universities and students tend to take positive action.Only when the investment return ratio is high enough, theenthusiasm of university students’ participation will be high.Therefore, universities need to improve training effectivenessfurther to increase the investment return ratio of universitystudents’ entrepreneurial ability improvement.


evolutionThe impact is shown in Figure 10, and the parameter value

selections are as follows: 𝑞 = 0.4, 𝐶𝐶

= 1, 𝐶𝑆= 10, 𝛼 =

0.2, 𝛾𝑆1

= 2, and 𝛾𝑆3

= 1.2.Figure 10 indicates that the rate of system convergence

increases with the growth of 𝛾𝑆2, with systematic evolution

transforming from mode (𝑀𝑌, 𝑁𝑌) to mode (𝑀

𝑁, 𝑁𝑁). So,

when making decision on participating in entrepreneurshiptraining or not, university students consider not only theinvestment return ratio, but also the opportunity costs of par-ticipation. It again showed that improvement training effec-tiveness further to increase the gains of university students’participation is the key to improve the students’ enthusiasmto participate in the entrepreneurial ability training.


evolutionFigure 11 shows the influence of return rate 𝛾

𝑆3of

enhancement of college students’ entrepreneurial ability on

system convergence.The parameters are listed as follows: 𝑞 =

0.4, 𝐶𝐶= 1, 𝐶

𝑆= 10, 𝛼 = 0.2, 𝛾

𝑆1= 2, and 𝛾

𝑆2= 1.5.

We may find that, in Figure 11, the impact of 𝛾𝑆3

onsystematic evolvement direction is similar to that of 𝛾

𝑆1on

the system; the impact of 𝛾𝑆3

on system convergence rate,however, is more obvious. It becomes slow with the increaseof 𝛾𝑆3. 𝑝0= 0.4 and 𝑝

0= 0.6 evolve in the direction towards

(𝑀𝑁, 𝑁𝑁) in the early periods and then in a short time they

change towards (𝑀𝑌, 𝑁𝑌) and converge at (𝑀

𝑌, 𝑁𝑌).

Further analysis finds that 𝛾𝑆1, 𝛾𝑆2, and 𝛾

𝑆3are decided

by the values of 𝛾𝑆1

− 𝛾𝑆3

and 𝛾𝑆2

− 𝛾𝑆3, which are further

decided by the balance of return rate and return rate of timeand energy used in other field, with or without assistanceby universities. A larger balance between 𝛾

𝑆1and 𝛾𝑆2

bringsthe evolvement to (𝑀

𝑌, 𝑁𝑌) in the ideal stage. But a larger

balance between 𝛾𝑆2and 𝛾𝑆3brings (𝑀

𝑌, 𝑁𝑌) more to a bad

lock mode. Anyway, higher investment of entrepreneurshiptraining leads to easier involvement to ideal mode. Hence,higher education institutions should take more efforts toenhance the efficiency in talent education so as to increasethe reward rate of students’ participation in the education.

(7) The impact of 𝛼 on the result of system evolutionFigure 12 shows the influence of return coefficient 𝛼 of

university entrepreneurship training on system convergence.Parameters are listed as follows: 𝑞 = 0.4, 𝐶

𝐶= 1, 𝐶

𝑆=

10, 𝛾𝑆1

= 2, 𝛾𝑆2

= 1.5, and 𝛾𝑆3

= 1.2.Figure 12 shows that, with the increase of return coeffi-

cient 𝛼, system converges faster to the ideal mode (𝑀𝑌, 𝑁𝑌)

and the systemwill change toward the ideal mode. In collegesand universities, the purpose of entrepreneurship educationand entrepreneurial ability is mainly to relieve employment


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

0 20 40

t

0 20 40

t

0 20 40

t

𝛾S3 = 0.7 𝛾S3 = 1.2 𝛾S3 = 1.4

Figure 11: The influence of the change of 𝛾𝑆3on the result of the system evolution.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

p0 = 0.1

p0 = 0.4

p0 = 0.6

p0 = 0.9

0 20 40

t

0 20 40

t

0 20 40

t

a = 0.15 a = 0.2 a = 0.3

Figure 12: The influence of return coefficient 𝛼 of university entrepreneurship training on system convergence.


pressure, and by conducting entrepreneurial education andtraining, to inspire students’ entrepreneurial enthusiasmand encourage students’ entrepreneurship. The purpose ofcultivating the ability of entrepreneurship is not only toencourage students to take part in the entrepreneurial activi-ties during their stay in school or after graduation, but also tofocus on the implementation of the students’ entrepreneurialpotential and help students accumulate human capitals andentrepreneurial energy stored for appropriate time for future.

6. Conclusion

Entrepreneurial talent training needs students’ positive par-ticipation. The purpose of this research is to investigatethe interaction between universities and students in theprocess of students’ entrepreneurial ability training and thesystem evolution law, in order to find effective strategiesfor promoting the enthusiasm and initiative of universitystudents’ entrepreneurial ability.

Through the construction of payoff matrix of students’behavior, the evolution of behavior interaction system, itsequilibrium, and the influence of different parameters on thesystem convergence are analyzed. The MatLab software isused for the results of numerical experiments under differentparameters of the evolution system. We found that modes(𝑀𝑌, 𝑁𝑌) and (𝑀

𝑁, 𝑁𝑁) are two evolutionary stable strate-

gies by the interaction between universities and students, andthe mode (𝑀

𝑁, 𝑁𝑁) is badly locked.

At present, students’ understanding of entrepreneurialability is insufficient. There exist some negative attitudestoward entrepreneurship education activity, which is notconducive to the improvement of students’ entrepreneurialability. Model analysis and numerical experiment show thatthe system can evolve towards ideal pattern through improv-ing the initial proportion of the positive involvement of groupselection of entrepreneurial talent training in universities,reducing investment cost of universities’ entrepreneurship,increasing the rate of return of universities’ entrepreneurshipeducation, stressing the investment on higher knowledge andability, or increasing the efficiency of the entrepreneurialability training to promote the reward rate of both universitiesand students.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This work was supported in part by the National Natu-ral Science Foundation of China under Grants 71373104and 71171099, the Jiangsu Philosophy and Societal Sci-ence Research Project under Grants 2012SJB630010 and2012SJB880021, the Soft Science Research Project of Zhen-jiang City under Grant YJ2012005, and the College Students’Ideological and Political Education Project of JiangsuUniver-sity under Grant JDXGCB201305.

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[2] A. Fayolle,Handbook of Research in Entrepreneurship Education,Edward Elegar, Northampton, Mass, USA, 2007.

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[8] D. A. Shepherd, “Educating entrepreneurship students aboutemotion and learning from failure,” Academy of ManagementLearning and Education, vol. 3, no. 3, pp. 274–287, 2004.

[9] K. Sudharson, A. M. Ali, and A. M. Sermakani, “An organiza-tional perspective of knowledge communication in developingentrepreneurship education for engineering students,”Procedia:Social and Behavioral Sciences, vol. 73, no. 27, pp. 590–597, 2013.

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