Lipschitz Games
arXiv:1107.1520 · doi:10.1287/moor.1120.0557
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 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.
minor changes, forthcoming in Mathematics of Operations Research
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