Coalition-Proof Equilibrium

We characterize the agreements that the players of a noncooperative game may reach when they can communicate prior to play, but they cannot reach binding agreements: A coalition-proof equilibrium is a correlated strategy from which no coalition has an improving and self-enforcing deviation. We show that any correlated strategy whose support is contained in the set of actions that survive the iterated elimination of strictly dominated strategies and weakly Pareto dominates every other correlated strategy whose support is contained in that set, is a coalition-proof equilibrium. Consequently, the unique equilibrium of a dominance solvable game is coalition-proof.