Approximation algorithms for indefinite quadratic programming
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Simple strategies for large zero-sum games with applications to complexity theory
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Game theory, on-line prediction and boosting
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
Playing large games using simple strategies
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The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computing correlated equilibria in multi-player games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Reducibility among equilibrium problems
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The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash Equilibria: Approximation and Smoothed Complexity
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Games of fixed rank: a hierarchy of bimatrix games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A Chernoff bound for random walks on expander graphs
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Fault tolerance in large games
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Computing Nash equilibria gets harder: new results show hardness even for parameterized complexity
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Repeated matching pennies with limited randomness
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Parameterized two-player nash equilibrium
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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We study multiplayer games in which the participants have access to only limited randomness. This constrains both the algorithms used to compute equilibria (they should use little or no randomness) as well as the mixed strategies that the participants are capable of playing (these should be sparse). We frame algorithmic questions that naturally arise in this setting, and resolve several of them. We give deterministic algorithms that can be used to find sparse Ɛ-equilibria in zero-sum and non-zero-sum games, and a randomness-efficient method for playing repeated zero-sum games. These results apply ideas from derandomization (expander walks, and δ-independent sample spaces) to the algorithms of Lipton, Markakis, and Mehta [LMM03], and the online algorithm of Freund and Schapire [FS99]. Subsequently, we consider a large class of games in which sparse equilibria are known to exist (and are therefore amenable to randomness-limited players), namely games of small rank. We give the first "fixed-parameter" algorithms for obtaining approximate equilibria in these games. For rank-k games, we give a deterministic algorithm to find (k + 1)-sparse Ɛ-equilibria in time polynomial in the input size n and some function f(k, 1/Ɛ). In a similar setting Kannan and Theobald [KT07] gave an algorithm whose run-time is nO(k). Our algorithm works for a slightly different notion of a game's "rank," but is fixed parameter tractable in the above sense, and extends easily to the multi-player case.