On nash-equilibria of approximation-stable games

Pranjal Awasthi, Maria Florina Balcan, Avrim Blum, Or Sheffet, Santosh Vempala

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations

Abstract

One reason for wanting to compute an (approximate) Nash equilibrium of a game is to predict how players will play. However, if the game has multiple equilibria that are far apart, or ε-equilibria that are far in variation distance from the true Nash equilibrium strategies, then this prediction may not be possible even in principle. Motivated by this consideration, in this paper we define the notion of games that are approximation stable, meaning that all ε-approximate equilibria are contained inside a small ball of radius Δ around a true equilibrium, and investigate a number of their properties. Many natural small games such as matching pennies and rock-paper-scissors are indeed approximation stable. We show furthermore there exist 2-player n-by-n approximation-stable games in which the Nash equilibrium and all approximate equilibria have support Ω(log n). On the other hand, we show all (ε,Δ) approximation-stable games must have an ε-equilibrium of support , yielding an immediate -time algorithm, improving over the bound of [11] for games satisfying this condition. We in addition give a polynomial-time algorithm for the case that Δ and ε are sufficiently close together. We also consider an inverse property, namely that all non-approximate equilibria are far from some true equilibrium, and give an efficient algorithm for games satisfying that condition.

Original languageEnglish
Title of host publicationAlgorithmic Game Theory - Third International Symposium, SAGT 2010, Proceedings
Pages78-89
Number of pages12
EditionM4D
DOIs
StatePublished - 2010
Externally publishedYes
Event3rd International Symposium on Algorithmic Game Theory, SAGT 2010 - Athens, Greece
Duration: 18 Oct 201020 Oct 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberM4D
Volume6386 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Symposium on Algorithmic Game Theory, SAGT 2010
Country/TerritoryGreece
CityAthens
Period18/10/1020/10/10

Bibliographical note

Funding Information:
This work was supported in part by NSF grants CCF-0830540 and CCF-0953192, ONR grant N00014-09-1-0751, and AFOSR grant FA9550-09-1-0538.

Funding

This work was supported in part by NSF grants CCF-0830540 and CCF-0953192, ONR grant N00014-09-1-0751, and AFOSR grant FA9550-09-1-0538.

FundersFunder number
National Science FoundationCCF-0830540, CCF-0953192
Office of Naval ResearchN00014-09-1-0751
Air Force Office of Scientific ResearchFA9550-09-1-0538

    Fingerprint

    Dive into the research topics of 'On nash-equilibria of approximation-stable games'. Together they form a unique fingerprint.

    Cite this