Lipschitz Games

The Lipschitz constant of a finite normal–form game is the maximal change in some player’s payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure -equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of pure -equilibrium. Our results shed new light on the large games literature: While the focus of that literature has been on anonymous games, our results imply that continuity, reflected by small Lipschitz constant, and not anonymity is the driving force behind the purification results. Therefore, the class of games that admit pure -equilibria is larger than what previous literature suggests, and contains in particular many network games.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Yaron Azrieli, Eran Shmaya
• Keywords: CORR 2011, Education, Lipschitz Constant, Single Opponent Changes, Small Lipschitz