Competitive outcomes and endogenous coalition formation in an n-person game

Sun N, Trockel W, Yang Z. Competitive outcomes and endogenous coalition formation in an n-person game. Working Papers. Institute of Mathematical Economics. Vol 358. Bielefeld: Universität Bielefeld; 2004.In this paper we study competitve outcomes and endogenous coalition formation in a cooperative n-person transferable utility (TU) game from the viewpoint of general equilibrium theory. For any given game, we construct a competitive exchange coalition production economy corresponding to the game. First, it is shown that the full core of a TU game is not empty if and only if the completion of the game is balanced. The full core is defined free of any particular coalition structure and the coalitions of the game emerge endogenously from the full core. Second, it is shown that the full core of a completion-balanced general TU game coincides with the set of equilibrium payoff vectors of its corresponding economy and that the coalition structures of the game are endogenously determined by the equilibrium outcomes of the economy. As a consequence, the core of a balanced general TU game coincides with the set of equilibrium payoff vectors of its corresponding economy