A Noncooperative Reformulation of the Core

The concept of the core is reformulated to handle externality problems where the total payoff for a coalition depends upon the actions of the players outside the coalition. A deviating coalition has rational expectations of the outsiders’ individual attempts to stop the deviation and their coalitional response if the deviaiton cannot be stopped, with the coalitional response itself a core solution among the outsiders. A noncooperative game of competing principals is designed and the set of its subgame perfect equilibria, with two refinement conditions, is equal to the reformulated core. Applied to a problem of pollution externality, the new concept of the core prescribes a way to maintain Pareto optimal cooperation without repeated games or a central planner. ∗Department of Economics, Iowa State University, 260 Heady Hall, Ames, IA 50011, [email protected], http://www.econ.iastate.edu/people/faculty/CV/669czheng.html.