Cores of games with positive externalities

This paper introduces a core concept, called the γ-core, in the primitive framework of a strategic game. For a certain class of strategic games, it is a weaker concept than the strong Nash equilibrium, but in general stronger than the conventional α- and β- cores. We argue that the coalition formation process is an infinitely repeated game and show that the grand coalition forms if the γ-core is nonempty. This is a weaker sufficient condition than the previous such condition (Maskin (2003, Theorem 4)). As an application of this result, it is shown that the γ- core of an oligopolistic market is nonempty and thus the grand coalition forms.