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We investigate the complexity of finding uniformly mixed Nash equilibria (that is, equilibria in which all played strategies are played with the same probability). We show that, even in very simple win/lose bimatrix games, deciding the existence of uniformly mixed equilibria in which the support of one (or both) of the players is at most or at least a given size is an NP-complete problem. Motivated...
We are interested in the complexity of finding Nash equilibria with one uniformly mixed strategy (that is, equilibria in which at least one of the players plays a uniform probability distribution over some set of pure strategies). We show that, even in imitation bimatrix games, where one player has a positive payoff if he plays the same pure strategy as the opponent, deciding the existence of such...
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