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Jason Abrevaya, Chair 2225 Speedway, Stop C3100, Austin, TX 78712 • Admin: 512-471-3211 & Advising: 512-471-2973

Eran Shmaya

Wed, April 7, 2010 • 3:30 PM - 5:00 PM • BRB 1.118

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Northwestern University, Kellogg School of Management

Pure Equilibria in Large Non-anonymous Games

Theory

Abstract: Recent literature shows that pure approximate Nash equilibria exist in anonymous and continuous large finite games. Here we study continuous but non-anonymous games. Call the emph{impact} of a game to the maximal difference in some player's payoff when one other player changes his strategy. We prove that small impact is exactly what guarantees existence of pure approximate equilibria. That is, we show that there is a threshold (which depends on the number of players and strategies in the game) such that pure approximate equilibria exist whenever the impact is less than this threshold. Further, whenever the impact is larger than the threshold there are arbitrarily large games with no pure approximate equilibria.


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