Lipschitz Games

Yaron Azrieli · Eran Shmaya

39 citations0/0 files storedMathematics of Operations Research

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Game Theory and Applications Game Theory and Voting Systems Evolutionary Game Theory and Cooperation

Abstract

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 ϵ-equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of a pure ϵ-equilibrium as a function of the number of players in the game and the number of strategies of each player. Our proofs use the probabilistic method.

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1996Potential Games 1973A class of games possessing pure-strategy Nash equilibria 1990Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities 1973Equilibrium points of nonatomic games 1991Comments on the Interpretation of Game Theory 2004Large Robust Games 2007Computing Equilibria in Anonymous Games 1983Equilibrium points of non-atomic games

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