Lipschitz Games

  • Authors:
  • Yaron Azrieli;Eran Shmaya

  • Affiliations:
  • Department of Economics, The Ohio State University, Columbus, Ohio 43210;Kellogg School of Management, Northwestern University, Evanston, Illinois 60208

  • Venue:
  • Mathematics of Operations Research
  • Year:
  • 2013

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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.