The Stability and Effectiveness of Climate Coalitions

A Comparative Analysis of Multiple Integrated Assessment Models


We report results from a comparison of numerically calibrated game theoretic integrated assessment models that explore the stability and performance of international coalitions for climate change mitigation. We identify robust results concerning the incentives of different nations to commit themselves to a climate agreement and estimate the extent of greenhouse gas mitigation that can be achieved by stable agreements. We also assess the potential of transfers that redistribute the surplus of cooperation to foster the stability of climate coalitions. In contrast to much of the existing analytical game theoretical literature, we find substantial scope for self-enforcing climate coalitions in most models that close much of the abatement and welfare gap between complete absence of cooperation and full cooperation. This more positive message follows from the use of appropriate transfer schemes that are designed to counteract free riding incentives.

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  1. 1.

    For a survey of this literature see Finus (2008), Eyckmans (2012) and Benchekroun and Long (2012).

  2. 2.

    Most models implement Pareto-efficiency through maximization of the utilitarian sum of individual welfare per region. MICA computes Pareto-efficient strategies by solving a competitive equilibrium on international commodity markets with full internalization of the climate change externality.

  3. 3.

    The strategy set in stage 2 depends on the specific features of the models. These range from choosing abatement directly to the indirect approach of choosing to invest in a broad variety of capital stocks (including energy and abatement technologies). See the appendix for details.

  4. 4.

    This notion of cartel stability was first applied to international environmental agreements by Hoel (1992), Carraro and Siniscalco (1993), and Barrett (1994).

  5. 5.

    We apply the procedure thus outlined for the models MICA, WITCH and RICE, for details see Kornek et al. (2014).

  6. 6.

    To be precise, the pure rates of time preference are constant in RICE and MICA, but diminish in WITCH from an initial 3–2 % over the course of a century.

  7. 7.

    Technically, the STACO model only considers benefits from abatement, and payoffs do not depend on the level of damages.

  8. 8.

    Since marginal damages are not entirely flat in any of the models but STACO, this procedure is just an approximation of the decomposition of the cooperative carbon price but since the abatement of the OECD coalition is unambitious and leakage is small, the error is negligible.

  9. 9.

    Specifically, we will refer to model regions EUR, EU, and OLDEURO as “Europe”.

  10. 10.

    Some models use a weighted sum in the social welfare function, see model factsheets in the Appendix.

  11. 11.

    In MICA, the largest share falls onto the rest-of-the-world (ROW) region, which includes several non-OECD countries.

  12. 12.

    Model regions Middle East and North Africa (MENA), Non-EU Eastern Europe (TE), and Sub Saharan Africa (SSA).

  13. 13.

    These are the most commonly used concepts for this set of models in previous studies. The analysis could be extended to include blocking power (or core stability) which, for the sake of brevity, we leave for future work.

  14. 14.

    Technically, this is because the STACO model is characterized by superadditivity, which means that the total worth of a group of players involved in a merger does not decrease, see Eyckmans et al. (2013) for details.

  15. 15.

    In two models, there is no single carbon price within the coalition (WITCH and RICE) because maximization of social welfare for the coalition balances marginal value of emissions in terms of utility but not monetary units. This is different in MICA (where international trade balances marginal utility of consumption) and CWS (which uses a linear utility function). In WITCH and RICE, we instead use the social cost of carbon for the conversion (computed as the marginal utility of carbon inside the coalition divided by the marginal utility of average per-capita consumption inside the coalition).


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We would like to thank all participants of the two workshops that led to this model comparison (Potsdam 8–9th of February, 2012, and Venice, 24–25th of January, 2013), and two anonymus reviewers for their helpful comments. We also benefited from feedback to presentations of the manuscript at Grantham Institute, LSE, at IGIER, Bocconi, and at the EAERE2013 conference, which is gratefully acknowledged. Ingram Jackard contributed to the review of numerical coalition models an preparation of the initial workshop, and we are grateful to Patrick Doupe, who helped us improve our style and presentation. Kai Lessmann received funding from the German Federal Ministry for Education and Research (BMBF promotion references 01LA1121A). The research work of Bosetti and Emmerling was supported by the Italian Ministry of Education, University and Research and the Italian Ministry of Environment, Land and Sea under the GEMINA project. The research work of Nagashima was supported by Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science, Grant Number 23730265.

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Correspondence to Kai Lessmann.

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Appendix: Model Factsheets

Appendix: Model Factsheets

Model: MICA (Model of International Climate Agreements), PIK, Germany
Model description: Kornek et al. (2013)
Model concept Solution method
Multi-region optimal growth model with climate externality and international trade Competitive equilibrium, full internalization of climate change damage within the coalition; implemented as non-linear optimization problem solved with a modified Negishi algorithm
Welfare concept Parametric specification
Discounted utilitarianism in each region, joint welfare maximization with constant Negishi weights for the coalition Pure rate of time preference \(\rho = 3\)%, elasticity of marginal utility \(\eta = 1\)
Markets and Trade Model anticipation
Consumption good Perfect foresight
Number of region: 11
AFR     Sub-Saharan Africa without South Africa
CHN    China
EUR     EU-27
IND     India
JPN     Japan
LAM    All American countries except Canada and the United States
MEA    North Africa, Middle Eastern and Arab Gulf countries, resource exporting countries within the former Soviet Union, and Pakistan
OAS     South East Asia, North Korea, South Korea, Mongolia, Nepal, Afghanistan
ROW    Australia, Canada, New Zealand, South Africa and non-EU27 European states except Russia
RUS     Russia
USA     United States of America
Base year Time horizon and step
2005 2005–2195, 10 years
Climate Climate change
Greenhouse Gases: CO\(_2\) Temperature response model
Carbon dioxide concentration (ppm)
Temperature change (\(^{\circ }\hbox {C}\))
Mitigation options Climate impacts
Abatement cost function for CO\(_2\) based on mitigation cost information from the REMIND model (Luderer et al. 2013) Region-specific quadratic damage function in temperature increase
Damage as [%] of GDP based on Fankhauser (1995) following Finus et al. (2006)
Land use Resources considered
Model: STACO-3 (Stability of Coalitions), Wageningen University, The Netherlands
Model description: Nagashima et al. (2011), Dellink et al. (2015)
Model concept Solution method
Combined game-theoretic and integrated assessment model with regional benefits (avoided damages) and abatement costs of greenhouse gas emissions Partial agreement Nash equilibrium between signatories and singletons
Welfare concept: Discounted net present value of regional payoff in each region, joint payoff maximization within coalitions; no full welfare evaluation but the Keynes–Ramsey rule used for discounting payoffs is consistent with a logarithmic utility function. Parametric specification: Pure rate of time preference \(\rho =1.5\)%; implicitly \(\eta =1\)
Markets and Trade Model anticipation
Carbon Trade is modelled as transfers between coalition members Perfect foresight
Number of region: 12
BRA    Brazil
CHN China
EUR EU and EFTA (EU-27, Iceland, Liechtenstein, Norway, Switzerland)
HIA     High-income Asia (Indonesia, Malaysia, Philippines, Singapore, South Korea, Taiwan, and Thailand)
IND     India
JPN Japan
MES    Middle Eastern countries
OHI     Other high income countries (including for example, Australia, Canada and New Zealand)
ROE     Rest of Europe
ROW    Rest of the world
RUS     Russia
USA     United States of America
Base year Time horizon and step
2011 2011–2106, 5 years
Climate Climate change
Greenhouse Gases: CO\(_2\), CH\(_4\), N\(_2\)O, PFCs, HFCs, SF\(_6\), based on EPPA-5 model to calibrate the regional GHGs BAU emission paths CO\(_2\)-e concentration (ppm) Radiative Forcing (W/m\(^2\))Temperature change (\({^{\circ }\hbox {C}}\))
Mitigation options: Regional abatement cost functions for GHGs are based on regional cost parameters from the EPPA model (Morris et al. 2008)
Climate impacts: Benefits are calculated as the net present value of the stream of future avoided damages from a unit of abatement in the current period, taking regional GDP growth and inertia in the climate system into account (Nagashima et al. 2011). This function is calibrated to a simple climate module, based on the DICE model (Nordhaus 2008), but calibrated on the EPPA-5 model (Paltsev et al. 2005; Paltsev 2010). The linear global benefit function is based on estimates of climate damage by Tol (2009). Benefits are allocated across regions with a share for each region (Finus et al. 2006).
Land use Resources considered
  1. Notes: Exogenous technological change (annual efficiency improvement in abatement costs) is considered to be \(0.5 - 2 \%\) per year (regionally differentiated)
Model: CWS (ClimNeg World Simulation model, Version 2.0), KU Leuven, Belgium
Model description: Bréchet et al. (2011)
Model concept Solution method
Multi-region optimal growth model with climate externality, maximization of coalition welfare, internalization of climate externality for coalition members Nash equilibrium of carbon emission game solved by tatonnement algorithm between coalition and non-members
Welfare concept Parametric specification
Discounted utilitarianism in each region, coalition’s welfare maximization with equal welfare weights for all members \(\rho = 1.5\)% (constant), \(\eta = 0\) (linear in consumption)
Markets and Trade Model anticipation
no trade in goods, trade in carbon emission permits (optional) Perfect foresight
Number of region: 6
USA:    United States of America
JAP:     Japan
EU:     South East Asia
China:   China
FSU:    Former Soviet Union
ROW:    Rest of the World
Base year Time horizon and step
2000 2000–2310, 10 years
Climate Climate change
Greenhouse Gases: CO\(_2\) 3-box model of carbon cycle (atmosphere, lower and upper ocean)
CO\(_{2}\)-e concentration (ppm)
Radiative Forcing (W/m\(^2\) )
Atmospheric and ocean temperature change (\(^{\circ }\hbox {C}\))
Mitigation options Climate impacts
Exogenous emission efficiency improvement over time plus region-specific abatement cost functions (power functions, exponent 2.887) Region-specific damage function, power function of atmospheric temperature change (exponent 3.0), damage as [%] of GDP
Land use Resources considered
Model: WITCH (World Induced Technical Change Hybrid model, version 2012), FEEM, Italy
Model description: Bosetti et al. (2014)
Model concept Solution method
Hybrid Optimal growth model, including a bottom-up energy sector and a simple climate model, embedded in a game theoretic setup Regional growth models solved by non-linear optimization and game theoretic setup solved by tatonnement algorithm between coalitions and non-members (Nash equilibrium)
Welfare concept Parametric specification
Discounted Utilitarianism, coalition’s welfare maximization with equal welfare weights for all members \(\rho = 3\)% decreasing, \(\eta = 1\) (log of consumption)
Markets and Trade Model anticipation
Oil Perfect foresight
Number of region: 13
CAJAZ:     Canada, Japan, New Zeland
CHINA:     China, including Taiwan
EASIA:     South East Asia
INDIA:     India
KOSAU:     South Korea, South Africa, Australia
LACA:     Latin America, Mexico and Caribbean
MENA:     Middle East and North Africa
NEWEURO:   EU new countries, CHE, NOR oldeuro: EU old countries (EU-15)
SASIA:     South Asia
SSA:     Sub Saharan Africa
TE:     Non-EU Eastern Europe, including Russia
USA:     United States of America
Base year Time horizon and step
2005 2005–2150, 5 years
Climate Climate change
Greenhouse Gases: 3-box model of carbon cycle
CO\(_2\), CH\(_4\), N\(_2\)O, HFCs, CFCs, SFs CO\(_2\)-e concentration (ppm)
Aerosols considered: yes Radiative Forcing (W/m\(^2\) )
Temperature change (\(^{\circ }\hbox {C}\))
Mitigation options Climate impacts
Abatement cost functions for non-CO2 GHGs Region-specific damage function with linear and power function term with exponent 2.2 in the temperature increase Damage as [%] of GDP
Land use  
Decarbonization options in the Energy system (Renewables, Nuclear, Biomass, CCS)  
Land use Resources considered
Emissions from land use change are considered Coal, Oil, Gas, Uranium, Biomass
Model: RICE Regional Integrated model of Climate and the Economy, SUNY Binghampton, USA
Model description Yang (2008)
Model concept Solution method
Multi-region Ramsey-type growth model with joint production of GHG emission that causes climate externality the non-cooperative Nash equilibrium; cooperative solutions under various assumptions of incentive compatibilities; coalition solutions (called “hybrid” Nash equilibria in Yang (2008))
Welfare concept Parametric specification
Discounted sum of regional utility functions. Pure rate of time preference \(\rho =3\)%, elasticity of marginal utility \(\eta =1\)
Markets and Trade Model anticipation
- Perfect foresight
Number of region: 6
CHN    China
EEC     Eastern European countries and the former Soviet Union
EU     European Union
OHI     Other high-income countries
ROW    Rest of the world
USA     United States of America
Base year Time horizon and step
2000 2000–2245 (5 years)
Climate Climate change
CO\(_2\) emissions and other exogenously set GHG emissions the Schneider box model
Mitigation options Climate impacts
Mitigation cost functions based on Nordhaus and Yang (1996) and updated with Yang (2008) which contains updates provided by Nordhaus Climate damage functions based on Nordhaus and Yang (1996) and updated with Yang (2008) which contains updates provided by Nordhaus
Land use Resources considered
exogenously set Availability of fossil fuel resources at global level has been checked implicitly

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Lessmann, K., Kornek, U., Bosetti, V. et al. The Stability and Effectiveness of Climate Coalitions. Environ Resource Econ 62, 811–836 (2015).

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  • Coalition stability
  • International environmental agreements
  • Numerical modeling
  • Transfers