The notion of the core is reformulated to handle externality problems where everyone's payoff may depend on the profile of actions across all players, inside or outside a coalition. Players may take actions through coalitional commitment, and the opportunity for commitment is allocated via open competition. Every coalition has rational expectations of the outsiders' reactions, which constitute a core solution among the outsiders. A decentralized noncooperative game of competing principals is designed and the set of its subgame perfect equilibria, with some refinement conditions, is equal to the reformulated core. In a problem of pollution externality that resembles Prisoners' Dilemma with n players, the Pareto optimum is the unique element in the core.
core, equilibrium, cooperative game theory, coalition, externality, competing principals
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