Playing large games using simple strategies
Proceedings of the 4th ACM conference on Electronic commerce
On the Complexity of Two-PlayerWin-Lose Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
Nash equilibria in random games
Random Structures & Algorithms
Approximate clustering without the approximation
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
New algorithms for approximate Nash equilibria in bimatrix games
Theoretical Computer Science
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
An optimization approach for approximate Nash equilibria
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
On the Complexity of Nash Equilibria and Other Fixed Points
SIAM Journal on Computing
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One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ε-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ε-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximationstable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ε,Δ) approximation-stable games must have an ε-equilibrium of support O(Δ2-o(1)/ε2 log n), yielding an immediate nO(Δ2-o(1)/ε2 log n) -time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ε are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.