Lipschitz games

Yaron Azrieli; Eran Shmaya

doi:10.1287/moor.1120.0557

Lipschitz games

Yaron Azrieli, Eran Shmaya

Managerial Economics, Decision Sciences and Operations

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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 .-equilibria, and pinpoint the maximal Lipschitz constant that is sufficient to imply existence of a pure .-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.

Original language	English (US)
Pages (from-to)	350-357
Number of pages	8
Journal	Mathematics of Operations Research
Volume	38
Issue number	2
DOIs	https://doi.org/10.1287/moor.1120.0557
State	Published - May 2013

Keywords

Large games
Lipschitz games
Pure equilibrium
Purification

ASJC Scopus subject areas

General Mathematics
Computer Science Applications
Management Science and Operations Research

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10.1287/moor.1120.0557

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AB - 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 a pure .-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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KW - Pure equilibrium

KW - Purification

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Lipschitz games

Abstract

Keywords

ASJC Scopus subject areas

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