The Existence of a Coalition-Proof Nash Equilibrium

Abstract

I provide two simple sufficient conditions under which the Pareto frontier of the Nash equilibrium set is coalition-proof. My first condition states there exists a pure-strategy Nash equilibrium which Pareto dominates all other serially undominated strategies. Under this condition, the Pareto-efficient Nash equilibrium is uniquely coalition- proof. I show that games with ordinal strategic complementarities which satisfy "ordinal monotone externalities" also satisfy the above condition. My second condition applies to games with strategic substitutabilities in equilibrium. Suppose that (1) the game has three players, or, a player's payoff depends only on his own strategy and the sum (but not the composition) of the opponents' strategies; and (2) the game has either positive externalities or negative externalities. Then the Pareto-efficient frontier of Nash equilibria is coalition-proof. Hence, under these two conditions, the common practice of the Pareto dominance refinement yields the same outcome as the coalition-proof Nash equilibrium refinement.

JEL Classification: C62, C72