Coalition-proofness and correlation with arbitrary communication possibilities

The ability of the members of a coalition to communicate secretly determines whether the coalition can coordinate to deviate from a proposed strategy and thus affects which strategies are ''coalition proof.'' We show that the existence of a Pareto-best element in the set of strategies that survive iterated elimination of dominated strategies implies the existence of a coalition-proof correlated equilibrium for any specification of coalitional communication possibilities that always permits individual deviations. Such an element exists in games with strategic complementarities if either (1) there is a unique Nash equilibrium or (2) each player's payoff is nondecreasing in the others' strategies. (C) 1996 academic Press, Inc.