Enumeration of all the extreme equilibria in game theory: bimatrix and polymatrix games
type: Item
instance of: scholarly article
title: Enumeration of all the extreme equilibria in game theory: bimatrix and polymatrix games
zbMATH Open document ID: 1122.91009
author: Charles Audet
author: Pierre Hansen
author: Slim Belhaiza
published in: Journal of Optimization Theory and Applications
publication date: 2007-03-06T00:00:00Z
review text: The autors study the problem of extreme Nash equilibria in bimatrix games and in their special generalization to \(n\)-person games, called polymatrix games . The first obtained result says that such games can be expressed as parametric linear 0-1 programs. Next this is used to construct the \(E\chi\)-MIP algorithm for the complete enumeration of the extreme equilibria in bimatrix and polymatrix games. This algorithm is numeracally illustrated for 3-person polymatrix games of size \(m\times m\times m\) with \(m\) up to 13. Also, it is compared with an another EEE algorithm of Audet in computational results on randomly generated bimatrix games for sizes \(n\times n\) for \(n\) up to 14.
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A06
Mathematics Subject Classification ID: 91B50
zbMATH DE Number: 5131136
zbMATH Keywords: Nash equilibria
reviewed by: Tadeusz Radzik
MaRDI profile type: Publication
full work available at URL: s10957-006-9070-3
OpenAlex ID: W2085259781
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DOI: 10.1007/S10957-006-9070-3
description: scientific article; zbMATH DE number 5131136