Limit Game Models for Climate Change Negotiations

  • Olivier Bahn
  • Alain HaurieEmail author
  • Roland Malhamé
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 15)


This paper deals with a family of dynamic game models that represent schematically the interaction between groups of countries in achieving the necessary limitation of carbon atmospheric emissions in order to control climate change. We start from a situation where m coalitions of countries exist and behave as m players in a game of sharing a global emission budget through the establishment of an international emissions trading system. We characterize the Nash equilibrium solutions for this game in a deterministic context. Through a simple replication schemes, we increase the number of players, each one becoming infinitesimal, and we characterize the limit games thus obtained. A stochastic version is proposed for this class of models, and the limit games are characterized, using the recently defined concept of mean field games.



This research has been supported by the Natural Sciences and Engineering Research Council of Canada (O. Bahn and R. Malhamé).


  1. 1.
    M.R. Allen, D.J. Frame, C. Huntingford, C.D. Jones, J.A. Lowe, M. Meinshausen, and N. Meinshausen. Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature, 458:1163–1166, 2009.Google Scholar
  2. 2.
    R. J. Aumann. Markets with a continuum of traders. Econometrica, 32:39–50, 1964.Google Scholar
  3. 3.
    F. Babonneau, A. Haurie, and M. Vielle. A robust meta-game for climate negotiations. Computational Management Science, 13:1–31, January 2013.Google Scholar
  4. 4.
    T. Başar and G.J. Olsder. Dynamic Noncooperative Game Theory. Academic Press, New York, 1995.Google Scholar
  5. 5.
    O. Bahn and A. Haurie. A class of games with coupled constraints to model international ghg emission agreements. International Game Theory Review, Vol. 10:337–362, 2008.Google Scholar
  6. 6.
    O. Bahn and A. Haurie. A cost-effectiveness differential game model for climate agreements. Dynamic Games and Applications, 6(1):1–19, 2016.Google Scholar
  7. 7.
    P.-N. Giraud, O. Guéant, J.-M. Lasry, and P.-L. Lions. A mean field game model of oil production in presence of alternative energy producers. mimeo 2010?Google Scholar
  8. 8.
    O. Guéant. A reference case for mean field games models. J. Math.Pures Appl., 92:276–294, 2009.Google Scholar
  9. 9.
    O. Guéant, J. M. Lasry, and P. L. Lions. Mean field games and oil production. Technical report, HAL, 2010.Google Scholar
  10. 10.
    S. Hallegatte, J. Rogelj, M. Allen, L. Clarke, O. Edenhofer, C.B. Field, P. Friedlingstein, L. van Kesteren, R. Knutti, K.J. Mach, M. Mastrandrea, A. Michel, J. Minx, M. Oppenheimer, G.-K. Plattner, K. Riahi, M. Schaeffer, T.F. Stocker, and D.P. van Vuuren. Mapping the climate change challenge. Nature Clim. Change, 6(7):663–668, 07 2016.Google Scholar
  11. 11.
    A. Haurie, F. Babonneau, N. Edwrads, P. Holden, A. Kanudia, M. Labriet, M. Leimbach, B. Pizzileo, and M. Vielle. Macroeconomics of Global Warming, chapter Fairness in Climate Negotiations : a Meta-Game Analysis Based on Community Integrated Assessment. Oxford Handbook, 2014.Google Scholar
  12. 12.
    A. Haurie and P. Marcotte. On the relationship between Nash-Cournot and Wardrop equilibria. Networks, 15:295–308, 1985.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    C. Helm. International emissions trading with endogenous allowance choices. Journal of Public Economics, 87:2737–2747, 2003.CrossRefGoogle Scholar
  14. 14.
    M. Huang, R. Malhamé, and P.E. Caines. Large population stochastic dynamic games: closed-loop Mckean-Vlasov systems and the nash certainty equivalence principle. Commun. Inf. Syst., 6(3):221–252, 2006.MathSciNetzbMATHGoogle Scholar
  15. 15.
    R. Knutti, J. Rogelj, J. Sedlacek, and E.M.Fischer. A scientific critique of the two-degree climate change target. Nature Geoscience, 9(1):13–18, January 2016.Google Scholar
  16. 16.
    J.-M. Lasry and P.-L. Lions. Mean field games. Japanese Journal of Mathematics, 2(1):229–260, 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    S. Mathesius, M. Hofmann, K. Caldeira, and Schellnhuber H.-J. Long-term response of oceans to co2 removal from the atmosphere. Nature Climate Change, 5(12):1107–1113, 2015.Google Scholar
  18. 18.
    J. Meadowcroft. Exploring negative territory carbon dioxide removal and climate policy initiatives. Climatic Change, 118(1):137–149, 2013.CrossRefGoogle Scholar
  19. 19.
    J. Rawls. A theory of justice. Harvard University Press, 1971.Google Scholar
  20. 20.
    M. Tavoni and R. Socolow. Modeling meets science and technology: an introduction to a special issue on negative emissions. Climatic Change, 118(1):1–14, 2013.CrossRefGoogle Scholar
  21. 21.
    K. Uchida. On the existence of Nash equilibrium point in n-person nonzero-sum stochastic differential games. SIAM Journal on Control and Optimization, 16(1):142–149.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.GERAD and Department of Decision SciencesHEC MontréalMontrealCanada
  2. 2.ORDECSYSChêne-BougeriesSwitzerland
  3. 3.University of GenevaGenevaSwitzerland
  4. 4.GERADHEC MontréalMontrealCanada
  5. 5.GERAD and Department of Electrical EngineeringPOLY MontréalMontrealCanada

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