文章基本信息

标题：Nash Equilibria in Perturbation-Stable Games
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作者：Maria-Florina Balcan ; Mark Braverman
期刊名称：Theory of Computing
印刷版ISSN：1557-2862
电子版ISSN：1557-2862
出版年度：2017
卷号：13
出版社：University of Chicago
摘要：Motivated by the fact that in many game-theoretic settings, the game analyzed is only an approximation to the game being played, in this work we analyze equilibrium computation for the broad and natural class of bimatrix games that are stable under perturbations. We specifically focus on games with the property that small changes in the payoff matrices do not cause the Nash equilibria of the game to fluctuate wildly. For such games we show how one can compute approximate Nash equilibria more efficiently than the general result of Lipton et al. (EC'03), by an amount that depends on the degree of stability of the game and that reduces to their bound in the worst case. Additionally, we show that for stable games, the approximate equilibria found will be close in variation distance to true equilibria, and moreover this holds even if we are given as input only a perturbation of the actual underlying stable game.For uniformly stable games, where the equilibria fluctuate at most quasi-linearly in the extent of the perturbation, we get a particularly dramatic improvement. Here, we achieve a fully quasi-polynomial-time approximation scheme, that is, we can find 1/poly(n)1/poly(n)-approximate equilibria in quasi-polynomial time. This is in marked contrast to the general class of bimatrix games for which finding such approximate equilibria is PPAD-hard. In particular, under the (widely believed) assumption that PPAD is not contained in quasi-polynomial time, our results imply that such uniformly stable games are inherently easier for computation of approximate equilibria than general bimatrix games.
关键词：algorithmic game theory; approximation algorithms; Nash equilibrium; beyond worst-case analysis; perturbation stability