A Game Theoretic Approach to North

South Collaboration

Ekko van IerlandWageningen University

based on joint work with Michael Finus, University of Hagen, Rob Dellink, Hans-Peter Weikard, Wageningen University and members of the STACO team

by

Need for sustainable development Globe exists for about 5-7 billion years

Human interaction with the environment needs to continue in a sustainable manner for several billions of years

Sustainable development: non-declining per capita welfare

Required: well balanced stocks of capital Human made capital (Savings and investment; new technologies) Natural capital (Efficient use of natural resources; new technologies) Human capital (Education! Education! inventions)

Brundtland report; Mäler; Pearce; …..

Global problems: Climate change For global problems no legal entities exist that can

enforce: we need voluntary international environmental agreements

How to reach agreement??Which countries will participate?How much emission reduction in each country?How to establish stable international coalition, e.g. Post-

Kyoto protocol?“It is not in our national interest to join the Kyoto protocol”

Barrett, Carraro, Finus, Ulph, Nordhaus, Dellink, Weikard, ..

Structure of the presentation 1. Introduction

2. Collaboration in Cartel formation Game

3. Empirical context

4. Analysis & Results: without and with transfers; renegotiations

5. Conclusions

Some warning at the start: Highly stylized analysis Reality differs from model analysis Setting of standard cost benefits analysis;discount rate 3% Focus on mitigation, not adaptation Impossible to explain all details in about 20 minutes; full

documentation in papers: See: www.enr.wur.nl/STACO

But…. valuable insights can be gained!

2. Cartel Formation Game for Climate

Protocol Coalition formation for 12 regions of the world non-cooperative approach: voluntary agreement cartel formation: one coalition and singletons test for internal and external stability of coalition

Pay-off

Pay-off DiscountingBenefits Abatement costs

Tt

i i it t it itt 1

(1 r ) (B (q ) AC (q ))

q is emission reduction of greenhouse gases

Theoretical background (cont.)1. Regions/countries indicate yes or no for a coalition2. Regions/countries choose abatement strategies: playing Nash against each other and the coalition Signatories maximize sum of pay-offs of coalition members;Signatories maximize sum of pay-offs of coalition members;

Singletons maximize their own pay offSingletons maximize their own pay off All consider the strategies of the other playersAll consider the strategies of the other players

Theoretical background (cont.) Testing for stability of coalition

Internal stability: no country wants to leave the coalition

External stability: no singleton wants to join the coalition

We test stability for 4084 possible coalitions; in case of multiple coalitions 4 million!

3. Empirical Modeling of global

warming Total stock of greenhouse gases in atmosphere according to Nordhaus’ DICE model

Total benefits

3 21 13 243.1 i i i i i iTAC q q q

( ) 1385.1 i i DTB q s q

t

t 2010 t s

t 2011 t pre ind 2010 pre ind s ss 2011

M q ,...,q M 1 M M 1 e q

Total abatement costs

Benefits per region : base caseRegion (i) Share in global benefits

si

1 USA 22.6 2 Japan 17.3 3 EU 23.6 4 Other OECD 3.5 5 Eastern Europe 1.3 6 Former Soviet Union 6.8 7 Energy Exporting countries 3.0 8 China 6.2 9 India 5.0 10 Dynamic Asian economies 2.5 11 Brazil 1.5 12 Rest of the World 6.8

Marginal abatement costs

0

500

1000

1500

2000

2500

3000

0 20 40 60 80 100 120 140 160 180 200 220 240

Q (Gton)

dis

co

un

ted

MA

C (

bln

$/G

ton

= $

/to

n)

Max. 132 Gton at 4564 $/ton

BRA

JPN

OOE

EET

DAE

EEX

EEC

FSU

ROW

IND

USA

CHN

EU

Source: Ellerman and Decaux (1998)

Schematic representation of emission

reduction

2010 2110Time

Em

issi

ons

(Gto

ns o

f C

O2)

Simple setting

Dynamic optimzed setting

4. Analysis & ResultsWe calculate what will happen for all coalitions, but

we report on the following:

Singleton coalition structure: no agreement at all Grand coalition structure: if all would participate! Industrialized countries structure: industrialised

countries No transfers: Stable coalition structure (Japan and

EU), but only if damage are 20% more than in base case.

Transfers by permit trading Renegotiations

Singleton coalition structure (Nash

equilibrium)Regions Average annualemissionreduction

Totalabatement

costs

Benefits minusabatement costs

Marginalabatement costs

percentage ofemissions in

2010

bln US$ over100 years

bln US$ over 100years

US$/ton CO2

USA 6.7 53 415 8.5JPN 1.4 2 354 6.5EU 4.7 24 464 8.8CHN 6.6 16 112 2.3

… … … … …ROW 5.3 4 137 2.5World 4.6 109 1,960 -

Global stock of carbon dioxide by 2110 = 1,561 gton

Grand coalition structureRegions Average annual

emissionreduction

Totalabatement

costs

Benefits minusabatement

costs

Marginalabatement

costs

Incentive to leavecoalition

percentage ofemissions in

2010

bln US$ over100 years

bln US$ over100 years

US$/ ton CO2 bln US$ over 100years

USA 15.7 513 1,656 37.4 23.6JPN 6.5 63 1,590 37.4 -123.8EU 11.5 229 2,033 37.4 -180.1CHN 40.6 1,348 -754 37.4 1133.2

… … … … … …ROW 26.5 250 401 37.4 185.1World 21.4 3,553 6,031 -

Global stock of carbon dioxide by 2110 = 1,475 gton

“Industrialized countries” (as intended)Regions Average annual

emission reduction

Total abatement

costs

Benefits minus abatement

costs

Marginal abatement

costs

Incentive to change

percentage of emissions in

2010

bln US$ over 100 years

bln US$ over 100 years

US$/ ton CO2 bln US$ over 100 years

USA* 13.4 332 574 28.0 65.3

JPN* 5.2 38 653 28.0 -46.9

EU* 9.7 147 798 28.0 -52.8 CHN 6.6 16 232 2.3 -794.9

… … … … … … ROW 5.3 4 268 2.5 -137.8

World 8.9 865 3,140 - -

Global stock of carbon dioxide by 2110 = 1,539 gton Note: * Coalition member

No transfers: Results for stable coalition (EU and

Japan)

Notes: * Coalition member

Level of damages increased in 20%

Regions Average annual emission reduction

Total abatement

costs

Benefits minus abatement

costs

Marginal abatement

costs

Incentive to change

percentage of emissions in

2010

bln US$ over 100 years

bln US$ over 100 years

US$/ ton CO2 bln US$ over 100 years

USA 7.5% 71 606 10.2 -80.1

JPN* 3.6% 17 498 18.3 -18.3

EU* 7.5% 76 629 18.3 -0.1

CHN 7.5% 22 163 2.8 -395.0

… … … … … … ROW 6.0% 5 198 3.1 -69.5

World 5.6% 203 2,784 - -

Global stock of carbon dioxide by 2110 = 1,556 gton

Global emissions reduction (% of base

year)

0

5

10

15

20

25

Singleton Industrializedcountries

Grand coalition Stable coalition(Japan and EU)

av

g.

an

nu

al

em

iss

ion

s r

ed

uc

tio

n (

%)

Damages increased

by 20%

Modify payoff function

Introducing transfers in the coalition: Permit

trading

* * * * *i i i i i i(q ,q ) (q ,q ) p (q q )

Emission permits* *

i i i i ii c i c i c

e e e e

BAU *i i i i

i c

q e e

thus

Initial allocation of permits (pragmatic

criteria)Scenario Operational rule

1) Quota BAUGrandfathering:proportion of emissions2010

2) Quota NashGrandfathering:proportion of emissions inNash equilibrium

Initial allocation of permits (equitable

criteria)Scenario Operational rule

3) Equal sharing Equal allocation

4) Egalitarian Allocation in proportion topopulation

5) Historicalresponsibility

Allocation in inverseproportion to emissions 2010

Initial allocation of permits (equitable

criteria)Scenario Operational rule

6) Ability to pay Allocation in inverseproportion to GDP per capita

7) Ability to pollute Allocation in inverseproportion to emissions percapita

8) Energy efficiency Allocation in inverseproportion to emissions perunit of GDP

Coalition EU-15 and CHN*

* This coalition is internally and externally stable under permit trading-quota BAU scenario. (1) ICM: Incentive to change membership.

Regions Totalemissionreduction

Payoffs(withoutpermittrading )

Payoffs(withpermittrading)

Transfers ICM(1)

(with permittrading)

gton (over100 years)

bln US$over 100years

bln US$over 100years

bln US$over 100years

bln US$over 100years

*iq iq i i

USA 16 - 683 683 - -132.6Japan 1 - 559 559 - -25.0EU-15 8 20 733 595 137 -131.3China 46 34 -6 131 -137 -19.3--- --- --- --- --- --- ---ROW 4 - 217 217 - -24.1World 87 - 2,942 2,942 - -

Permit Price = MACic =11 US$/ton

Coalition EU-15 and CHN*

* This coalition is internally and externally stable under permit trading-quota BAU scenario. (1) ICM: Incentive to change membership.

Regions Total emission reduction

Payoffs (without permit

trading )

Payoffs (with

permit trading)

Transfers ICM(1) (with

permit trading)

gton (over 100 years)

bln US$ over 100

years

bln US$ over 100

years

bln US$ over 100

years

bln US$ over 100

years *

iq iq i i

USA 16 - 683 683 - -132.6 Japan 1 - 559 559 - -25.0 EU-15 8 20 733 595 137 -131.3 China 46 34 -6 131 -137 -19.3 --- --- --- --- --- --- --- ROW 4 - 217 217 - -24.1 World 87 - 2,942 2,942 - -

Permit Price = MACic =11 US$/ton

Stable coalitions, if transfers are used

0

1000

2000

3000

4000

5000

6000

7000

Singleton coalition EU-15,China India, ROW EU-15, EE, India Japan, India Grand coaliton

Glo

bal

ben

efi

ts (

bil

lio

n U

S $

)

Renegotiations

What will happen if renegotiations occur? For instance after 50 years… Or every 20 years …..

Which coalitions will be stable in early commitment periods and in later periods?

Results: more often renegotiations

1st commitment period

2nd commitment period

3rd commitment period

4th comm. period

5th comm. period

Total payoff

USA/EET/FSU/EEX/CHN/DAE/ROW EU-15/EEX/CHN EU-15/EET/CHN USA/CHN USA/CHN 8824

USA/OOE/EET/FSU/CHN/DAE/ROW EU-15/EEX/CHN EU-15/EET/CHN USA/CHN USA/CHN 8801

USA/EET/FSU/EEX/CHN/DAE/ROW EU-15/EET/CHN EU-15/EET/CHN USA/CHN USA/CHN 8785

EU-15/OOE/EET/EEX/CHN/IND/ROW USA/EET/CHN EU-15/EET/CHN USA/CHN USA/CHN 8758

EU-15/EET/EEX/CHN/IND/DAE/ROW USA/EET/CHN EU-15/EET/CHN USA/CHN USA/CHN 8755

EU-15/OOE/EET/FSU/EEX/CHN/IND USA/EET/CHN EU-15/EET/CHN USA/CHN USA/CHN 8754

EU-15/EET/FSU/EEX/CHN/IND/DAE USA/EET/CHN EU-15/EET/CHN USA/CHN USA/CHN 8751

EU-15/OOE/EET/CHN/IND/DAE/ROW USA/EET/CHN EU-15/EET/CHN USA/CHN USA/CHN 8731

EU-15/OOE/EET/FSU/CHN/IND/DAE USA/EET/CHN EU-15/EET/CHN USA/CHN USA/CHN 8727

USA/OOE/EET/EEX/CHN/DAE/ROW EU-15/EEX/CHN EU-15/EET/CHN USA/CHN USA/CHN 8718

{1542 RPE sequences in total}

An optimal transfer scheme Optimal transfer scheme: any scheme that fully uses the

gains from cooperation to enhance stability

Based on surplus sharing not some exogenous rule, such as emissions (as above) the surplus is shared according to “outside option payoffs”,

i.e. how much a region would get if it were to deviate

Maximises internal stability if coalitional surplus exceeds outside option payoffs,

internal stability is guaranteed external stability of course not guaranteed

Renegotiations and an optimal transfer

scheme Renegotiations after 50 years (50 + 50 years) Optimal transfers generate multiple equilibria (626) in

second stage, and large number (35671) of stable coalitions in 1st stage

Best performing: USA, EU-15, EET, EEX, CHN, IND in first stage and EU-15, EET, EEX, CHN, IND in second stage (providing 57% of potential gains from cooperation)

Renegotiations after 20 years (20 + 80 years) Best performing: Grand coalition (!) in first stage and

EU-15, EET, EEX, CHN, IND in second stage (59% of potential gains)

Conclusions (I of IV) How to reach

agreement? Highly stylized model; it assists in explaining international

negotiations: strong free rider incentives!; but gains from cooperation can be large!

Empirical analysis for non-symmetric regions without transfers provides only 1 internally and externally stable coalition: EU and Japan at 1.2 time benchmark damages

“Industrialised countries” reduce 8.9%; Singletons 4.8%; EU-Japan 5.6%, as compared to 2010 level.

Grand coalition in our setting would reduce emissions by 21%, but restricted time horizon and low damages.

Conclusions (II of IV) How to reach agreement? In cartel setting without transfers, coalition formation will

be very difficult in practice, because free rider incentives dominate!

With transfers, and no renegotiations, only a few small coalitions are stable and they reach relatively little as compared to the singleton case.

Conclusions (III of IV) How to reach

agreement? With renegotiations, larger coalitions can be stable, even

the grand coalition in the first period. Substantial results can be reached.

If countries only act on the basis of self-interest not all gains can be obtained

Responsible governments should go for a grand coalition and will share benefits on equity principles.

This requires willingness to cooperate and to accept sanctions if free riding would occur.

Conclusions (IV of IV) How to reach

agreement? Further climate related catastrophes, unless in international

politics adequate policy measures are agreed upon. In Grand coalition global welfare is optimized: we need to

search for such arrangement with USA and others If a grand coalition is impossible, multiple coalitions can be

helpful, as long as all major players make a substantial contribution.

Special note: Climate change will be irreversible and very harmful: no scope for discounting future damages!

Without international cooperation on climate change no sustainable development.

STACO PROJECT

http://www.enr.wur.nl

Environmental Economics and Natural Resources Group

Wageningen University

Thanks!

Free Rider Incentive IndexRegion Free rider incentive index1 USA 4.7%2 Japan 2.6%3 EU 3.3%4 Other OECD 32.4%5 Eastern Europe 100.0%6 Former Soviet Union 19.7%7 Energy Exporting countries 23.7%8 China 45.0%9 India 45.4%10 Dynamic Asian economies 71.2%11 Brazil 23.4%12 Rest of the World 27.0%

Sensitivity analysis for calibration IScenario Benchmarks Total

emissionreduction

Average annualemissionreduction

Totalabatement

costs

Total benefitsfrom

abatement

Benefits minusabatement

costs

gton (over100 years)

percentage ofemissions in

2010

bln US$over 100

years

bln US$ over100 years

bln US$ over100 years

no cooperation 34 2.9 36 644 608benefits 50 % coalition JPN, EU - - - - -

full cooperation 172 14.4 1,225 3,211 1,986

no cooperation 55 4.6 109 2,069 1,960benefits 100 % coalition JPN, EU - - - - -

full cooperation 256 21.4 3,553 9,584 6,031

no cooperation 62 5.2 145 2,801 2,655benefits 120 % coalition JPN, EU 67 5.6 203 2,988 2,784

full cooperation 284 23.8 4693 12,746 8,053

Sensitivity analysis for calibration I

(cont.)Scenario Benchmarks Totalemissionreduction

Average annualemissionreduction

Totalabatement

costs

Total benefitsfrom

abatement

Benefits minusabatement

costs

gton (over100 years)

percentage ofemissions in

2010

bln US$over 100

years

bln US$ over100 years

bln US$ over100 years

no cooperation 62 5.2 145 2,801 2,655benefits 120 % coalition JPN, EU 67 5.6 203 2,988 2,784

full cooperation 284 23.8 4693 12,746 8,053

no cooperation 87 7.3 324 6,485 6,161benefits 200 % coalition JPN, EU 92 7.7 455 6,908 6,453

full cooperation 377 31.5 10,204 28,205 18,000

no cooperation 112 9.3 609 12,519 11,910benefits 300 % coalition JPN, EU 119 9.9 857 13,323 12,466

full cooperation 470 39.3 18,856 52,759 33,903

Future research Test for open and exclusive membership Test for transfer schemes Test for multiple coalition structures

e.g. {1,1,2,2,3,3,3,} Analyze technology spillover Anlyze impacts if lobby groups Test for uncertainty on parameter values Allow for more periods Test for multiple deviations Improve regional damage estimates!

Advantage of model: simplicity of specification allows for huge number of coalition structures to be calculated