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Abstract: In this paper, we study nonzero-sum separable games, which are continuousgames whose payoffs take a sum-of-products form. Included in this subclass areall finite games and polynomial games. We investigate the structure ofequilibria in separable games. We show that these games admit finitelysupported Nash equilibria. Motivated by the bounds on the supports of mixedequilibria in two-player finite games in terms of the ranks of the payoffmatrices, we define the notion of the rank of an n-player continuous game anduse this to provide bounds on the cardinality of the support of equilibriumstrategies. We present a general characterization theorem that states that acontinuous game has finite rank if and only if it is separable. Using our rankresults, we present an efficient algorithm for computing approximate equilibriaof two-player separable games with fixed strategy spaces in time polynomial inthe rank of the game.



Author: Noah D. Stein, Asuman Ozdaglar, Pablo A. Parrilo

Source: https://arxiv.org/







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