We give simple proofs of refinements of the complexity results of Gilboa and Zemel (1989), and we derive additional results of this sort. Our constructions employ imitation games, which are two person games in which both players have the same sets of pure strategies and the second player wishes...

TAn imitation game is a finite two person normal form game in which the two players have the same set of pure strategies and the goal of the second player is to choose the same pure strategy as the first player. Gale et al. (1950) gave a way of passing from a given two person game to a symmetric...