A Game of International Climate Policy Solved by a Homogeneous Oracle-Based Method for Variational Inequalities

  • Laurent Drouet
  • Alain Haurie
  • Jean-Philippe Vial
  • Marc Vielle
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 11)


This paper presents a game-theoretic model for the international negotiations that should take place to renew or extend the Kyoto protocol beyond 2012. These negotiations should lead to a self-enforcing agreement on a burden sharing scheme to realize the necessary global emissions abatement that would preserve the world against irreversible ecological impacts. The model assumes a noncooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model is solved using an homogeneous version of the oracle-based optimization engine (OBOE) permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3.


Nash Equilibrium Variational Inequality Computable General Equilibrium Marginal Abatement Cost Cumulative Emission 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Armington, P.S.: A theory of demand for products distinguished by place of production. IMF Staff Papers 16, 159–178 (1969)Google Scholar
  2. 2.
    Bernard, A., Haurie, A., Vielle, M., Viguier, L.: A two-level dynamic game of carbon emission trading between Russia, China, and Annex B countries. Journal of Economic Dynamics and Control 32(6), 1830–1856 (2008)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bernard, A., Vielle, M.: Comment allouer un coût global d’environnement entre pays : permis négociables versus taxes ou permis négociables et taxes? Économie Internationale 82, 103–135 (2000)Google Scholar
  4. 4.
    Bernard, A., Vielle, M.: Measuring the welfare cost of climate change policies: A comparative assessment based on the computable general equilibrium model GEMINI-E3. Environmental Modeling & Assessment 8(3), 199–217 (2003)CrossRefGoogle Scholar
  5. 5.
    Bernard, A., Vielle, M.: GEMINI-E3, a General Equilibrium Model of International National Interactions between Economy, Energy and the Environment. Computational Management Science 5(3), 173–206 (2008)MATHMathSciNetGoogle Scholar
  6. 6.
    Bernard, A., Vielle, M., Viguier, L.: Carbon tax and international emissions trading: A swiss perspective. In Haurie, A., Viguier, L. (eds.) Coupling Climate and Economic Dynamics. Springer (2005)Google Scholar
  7. 7.
    Dimaranan, B.V.: Global Trade, Assistance, and Production: The GTAP 6 Data Base. Center for Global Trade Analysis Purdue University, Center for Global Trade Analysis, Purdue University (2006)Google Scholar
  8. 8.
    Drouet, L., Haurie, A., Moresino, F., Vial, J.-P., Vielle, M., Viguier, L..: An oracle based method to compute a coupled equilibrium in a model of international climate policy. Computational Management Science 5(1), 119–140 (2008)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ferris, M.C., Munson, T.S.: Complementarity problems in GAMS and the PATH solver. Journal of Economic Dynamics and Control 24, 165–188 (2000)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ferris, M.C., Pang, J.S.: Complementarity and Variational Problems: State of the Art. IAM Publications, Philadelphia (1997)MATHGoogle Scholar
  11. 11.
    Haurie, A.: Environmental coordination in dynamic oligopolistic markets. Group Decision and Negotiation 4, 46–67 (1995)CrossRefGoogle Scholar
  12. 12.
    Haurie, A., Krawczyk, J.: Optimal charges on river effluent from lumped and distributed sources. Environmental Modeling and Assessment 2, 177–199 (1997)CrossRefGoogle Scholar
  13. 13.
    Haurie, A., Smeers, Y., Zaccour, G.: Stochastic equilibrium programming for dynamic oligopolistic markets. Journal of Optimmization Theory and Applications 66(2) (1990)Google Scholar
  14. 14.
    Haurie, A., Zaccour, G.: Game-theoretic models of the environment. In: Annals of the International Society of Dynamic Games, volume 3, chapter Differential game models of global environmental management, pages 3–23. Birkhäuser, Boston (1995)Google Scholar
  15. 15.
    Krawczyk, J.B.: Coupled constraint Nash equilibria in environmental games. Resource and Energy Economics 27(2), 157–181 (2005)CrossRefGoogle Scholar
  16. 16.
    Krawczyk, J.B.: Numerical solutions to coupled-constraint (or generalised Nash) equilibrium problems. Computational Management Science 2(1), 183–204 (2007)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Loulou, R.: ETSAP-TIAM: the TIMES integrated assessment model. part ii: mathematical formulation. Computational Management Science 5(3), 41–66 (2008)Google Scholar
  18. 18.
    Nesterov, Y., Nemirovsky, A.: Interior Point Polynomial Methods in Convex Programming. SIAM, Philadelphia (1994)Google Scholar
  19. 19.
    Nesterov, Y., Vial, J.-P.: Homogeneous Analytic Center Cutting Plane Methods for convex problems and variational inequalities. SIAM J. Optim. 9(3), 707–728 (1999)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Nesterov, Y., Péton, O., Vial, J.-P.: Homogeneous Analytic Center Cutting Plane Methods with approximate centers. Optimization Methods and Software 11&12, 243–273 (1999)CrossRefGoogle Scholar
  21. 21.
    Pang, J.S., Fukushima, M.: Quasi-variational inequalities, generalized Nash equilibria and multi-leader-follower games. Computational Management Science 2(1), 21–56 (2005)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Péton, O. The homogeneous analytic center cutting plane method. Ph.D. Thesis, Université de Genève (2002)Google Scholar
  23. 23.
    Rosen, J.B.: Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33(3), 520–534 (1965)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Stern, N.: Stern Review: The Economics of Climate Change. HM Treasury UK, London (2006)Google Scholar
  25. 25.
    Stone, J.R.N.: Linear expenditure systems and demand analysis: An application to the pattern of british demand. Economic Journal (1983)Google Scholar
  26. 26.
    von Heusinger, A., Kanzow, C.: SC optimization reformulations of the generalized Nash equilibrium problem. Optimization Methods and Software 23, 953–973 (2008)MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    von Heusinger, A., Kanzow, C.: Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions. Computational Optimization and Applications 43, 353–377 (2009)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Laurent Drouet
    • 1
  • Alain Haurie
    • 2
  • Jean-Philippe Vial
    • 3
    • 4
  • Marc Vielle
    • 5
    • 6
  1. 1.Resource Centre for Environmental Technologies, Public Research Centre Henri TudorTechnoport SchlassgoartEsch-sur-AlzetteLuxembourg
  2. 2.ORDECSYSChêne-BougeriesSwitzerland
  3. 3.University of GenevaGenevaSwitzerland
  4. 4.ORDECSYSChêne-BougeriesSwitzerland
  5. 5.École Polytechnique Fédérale de Lausanne and C-ORDEEEcublensFrance
  6. 6.Toulouse School of Economics (LERNA)TSE - Manufacture de TabacsToulouseFrance

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