In a game with positive externalities, such as e.g. the standard environmental externality game, the set of imputations having the property of internal stability, when such a set exists, is a subset of the gamma-core, that is, the set of imputations with the property of gamma-core stability. The key argument that drives the result rests on the concept, introduced here, of “acceptability” by a coalition of ensuring its members their free rider payoff, and on linking it with the notion of “blocking” in the theory of the core. It is first presented graphically, then analytically. The hierarchy thus presented between core stability and internal stability triggers some concluding thoughts on efficiency, coalitional stability, and the possible sources of cooperation in international environmental issues.
Tulkens, H. (2014). Internal vs. core coalitional stability in the environmental externality game: A reconciliation (CORE Discussion Papers 2014/58). https://hdl.handle.net/2078.5/194542