English

Lipschitz Games

Combinatorics 2013-09-24 v2 Computer Science and Game Theory

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 {\epsilon}-equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of pure {\epsilon}-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.

Keywords

Cite

@article{arxiv.1107.1520,
  title  = {Lipschitz Games},
  author = {Yaron Azrieli and Eran Shmaya},
  journal= {arXiv preprint arXiv:1107.1520},
  year   = {2013}
}

Comments

minor changes, forthcoming in Mathematics of Operations Research

R2 v1 2026-06-21T18:33:48.491Z