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Settling the complexity of computing two-player Nash equilibria
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New algorithms for approximate Nash equilibria in bimatrix games
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New algorithms for approximate Nash equilibria in bimatrix games
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An optimization approach for approximate Nash equilibria
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Polynomial algorithms for approximating nash equilibria of bimatrix games
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On the complexity of approximating a Nash equilibrium
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On mutual concavity and strategically-zero-sum bimatrix games
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Well supported approximate equilibria in bimatrix games: a graph theoretic approach
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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On the communication complexity of approximate nash equilibria
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In view of the intractability of finding a Nash equilibrium, it is important to understand the limits of approximation in this context. A subexponential approximation scheme is known [LMM03], and no approximation better than is possible by any algorithm that examines equilibria involving fewer than logn strategies [Alt94]. We give a simple, linear-time algorithm examining just two strategies per player and resulting in a -approximate Nash equilibrium in any 2-player game. For the more demanding notion of well-supported approximate equilibrium due to [DGP06] no nontrivial bound is known; we show that the problem can be reduced to the case of win-lose games (games with all utilities 0–1), and that an approximation of is possible contingent upon a graph-theoretic conjecture.