Internal vs. core coalitional stability in the environmental externality game: A reconciliation

In a game with positive externalities, such as e.g. the standard environmental externality game used in the analysis of international environmental agreements, the solutions having the property of coalitional internal stability, when they exist, are compared in this paper with the solutions with the property of ?-core stability. Key instruments for that comparison are the notions of stable imputations, on the one hand, and on the other, of partial agreement Nash equilibria relative to a coalition as they result from unacceptable, i.e. unstable imputations. The relation between internal and core stable solutions is claimed to be one of compatibility, the former concept complementing the latter in the games where internally stable solutions exist. But this class of games is more restricted than the one for which only ?-core solutions exist. The argument is first presented graphically, then analytically. The relations here exhibited between core and internal forms of stability arouse some concluding thoughts on efficiency, coalitional stability, and on motivations in sharing the surplus generated by cooperation in international environmental issues