The alternative of cooperation vs. non-cooperation is a central issue in the analysis and the understanding of international environmental agreements relating to climate change. It has been much studied by means of game theoretic tools, applied most often to static economic models – although the climate change problem is essentially of dynamic nature, due to the accumulating nature of the emitted CO2. When more realistic dynamic economic models are formulated, non cooperative dynamic games associated with them are available in the literature, but cooperative counterparts can hardly be found – which sometimes induces doubts as to the relevance of game theory in explaining existing agreements.

Elaborating on previous results [1], [2], and [3] the present paper formulates a dynamic economic-environmental model in discrete time, to which a (discrete time) dynamic game is associated. Within the time path  of the game’s solution the alternative of non cooperation vs. cooperation is dealt with at each time sub-period in terms of subgames for which either internally stable Nash equilibria of various sorts (in the sense initiated in [4]), or coalitionally stable ?-core outcomes in the sense of [5], are defined. The cooperative solution to the dynamic game, specified for both finite and infinite horizons, is then proposed and exhibited as a sequence of the said stable ?-core outcomes. Alternative partially cooperative solutions are examined in the same way.

Economically and policy wise, this construction suggests that an internal logic can be called upon to both explain the forms of cooperation between countries, and inspire a long term view, as sketched out in [6], of the ongoing negotiations process initiated by the UNFCCC.

References to relevant earlier works :
For the rational expectations interpretation of closed loop modeling and computation of solutions :
[1] GERMAIN, M., TOINT, Ph. and TULKENS, H. 1998, "Stabilité stratégique en matière de pollution internationale avec effet de stock:le cas linéaire", Revue Economique (Paris) 49 (6), 1435-1454. CORE Reprint 1351.
[2]* GERMAIN, M., TOINT, Ph., TULKENS, H. and de ZEEUW, A. 2003, "Transfers to Sustain Dynamic Core-Theoretic Cooperation in International Stock Pollutant Control", Journal of Economic Dynamics and Control 28 (2003), 79-99. CORE Reprint 1637.
[3] GERMAIN, M., TULKENS, H. and MAGNUS, A. 2010, “Dynamic core-theoretic cooperation in a two-dimensional international environmental model”, Mathematical Social Sciences 59 (2010), 208-226. CORE Reprint 2218.
For internally stable partial agreement Nash equilibria and the gamma-core in the static model:
[4] CARRARO, C. and D. SINISCALCO (1993), “Strategies for the International Protection of the Envi-ronment”, Journal of Public Economics 52, 309-328.
[5]* CHANDER, P. and TULKENS, H. 1997, "The Core of an economy with multilateral environmental externalities", International Journal of Game Theory 26, 379-401. CORE Reprint 1276.
For policy implications:
[6]* CHANDER, P. and TULKENS, H. 2011, “The Kyoto Protocol, the Copenhagen Accord, the Cancun Agreements, and beyond: An economic and game theoretical exploration and interpretation”, CORE Discussion Paper 2011/ 51 (October).
*These papers are reprinted in CHANDER, P., DRÈZE, J., LOVELL, C.K. and MINTZ, J. (eds) 2006, Public goods, environmental externalities and fiscal competition: essays by Henry Tulkens, Springer, New York.

This seminar has been jointly organized by FEEM and CMCC.