Iterated Elimination of Dominated Mixed Strategies

Abstract

This note compares two iterated dominance procedures, one based on eliminating mixed strategies and one based on eliminating pure strategies. It shows that, in compact and continuous games, the mixed-strategy procedure can trail the pure-strategy procedure by at most one round: If the pure-strategy procedure terminates at round $M$, the mixed-strategy procedure terminates at either $M$ or $M+1$, and this bound is tight. It also provides two characterizations of the mixed-strategy procedure that are round-for-round equivalent to it and that require checking for improvements only against opponents' pure strategies.