Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Reducibility among equilibrium problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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
Approximating nash equilibria using small-support strategies
Proceedings of the 8th ACM conference on Electronic commerce
Progress in approximate nash equilibria
Proceedings of the 8th ACM conference on Electronic commerce
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Games of fixed rank: a hierarchy of bimatrix games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Equilibria in Anonymous Games
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Discretized Multinomial Distributions and Nash Equilibria in Anonymous Games
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
New algorithms for approximate Nash equilibria in bimatrix games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
An optimization approach for approximate Nash equilibria
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Polynomial algorithms for approximating nash equilibria of bimatrix games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
A note on approximate nash equilibria
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Partially-Specified large games
WINE'05 Proceedings of the First international conference on Internet and Network Economics
On oblivious PTAS's for nash equilibrium
Proceedings of the forty-first annual ACM symposium on Theory of computing
Learning poisson binomial distributions
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Survey: Nash equilibria: Complexity, symmetries, and approximation
Computer Science Review
Ranking games that have competitiveness-based strategies
Theoretical Computer Science
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We present a novel polynomial time approximation scheme fortwo-strategy anonymous games, in which the players’ utilityfunctions, although potentially different, do not differentiateamong the identities of the other players. Our algorithm computesan ε-approximate Nash equilibrium of an n-player 2-strategyanonymous game in time $\text{poly}(n) \cdot(1/\epsilon)^{O(1/\epsilon^2)}$, which significantly improves uponthe running time $n^{O(1/\epsilon^2)}$ required by the algorithm ofDaskalakis & Papadimitriou, 2007. The improved running time isbased on a new structural understanding of approximate Nashequilibria: We show that, for any ε, there exists anε-approximate Nash equilibrium in which either onlyO(1/ε 3) players randomize, or all players who randomizeuse the same mixed strategy. To show this result we employ toolsfrom the literature on Stein’s Method.