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We consider Nash equilibria in 2-player random games and analyze a simple Las Vegas algorithm for finding an equilibrium. The algorithm is combinatorial and always finds a Nash equilibrium; on m × n payoff matrices, it runs in time O(m2n log log n + n2m log log m) with high probability. Our main tool is a polytope formulation of equilibria.
Date of Conference: 23-25 Oct. 2005