Enumeration of all the extreme equilibria in game theory: Bimatrix and polymatrix games

C. Audet; S. Belhaiza; P. Hansen

doi:10.1007/s10957-006-9070-3

Enumeration of all the extreme equilibria in game theory: Bimatrix and polymatrix games

C. Audet^*, S. Belhaiza, P. Hansen

^*Corresponding author for this work

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

31 Scopus citations

Abstract

Bimatrix and polymatrix games are expressed as parametric linear 0-1 programs. This leads to an algorithm for the complete enumeration of their extreme equilibria, which is the first one proposed for polymatrix games. The algorithm computational experience is reported for two and three players on randomly generated games for sizes up to 14 x 14 and 13 x 13 x 13.

Original language	English
Pages (from-to)	349-372
Number of pages	24
Journal	Journal of Optimization Theory and Applications
Volume	129
Issue number	3
DOIs	https://doi.org/10.1007/s10957-006-9070-3
State	Published - Jun 2006
Externally published	Yes

Keywords

Bimatrix games
Enumeration
Extreme equilibria
Nash equilibria
Polymatrix games

ASJC Scopus subject areas

Management Science and Operations Research
Control and Optimization
Applied Mathematics

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10.1007/s10957-006-9070-3

Cite this

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title = "Enumeration of all the extreme equilibria in game theory: Bimatrix and polymatrix games",

abstract = "Bimatrix and polymatrix games are expressed as parametric linear 0-1 programs. This leads to an algorithm for the complete enumeration of their extreme equilibria, which is the first one proposed for polymatrix games. The algorithm computational experience is reported for two and three players on randomly generated games for sizes up to 14 x 14 and 13 x 13 x 13.",

keywords = "Bimatrix games, Enumeration, Extreme equilibria, Nash equilibria, Polymatrix games",

author = "C. Audet and S. Belhaiza and P. Hansen",

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AU - Audet, C.

AU - Belhaiza, S.

AU - Hansen, P.

PY - 2006/6

Y1 - 2006/6

N2 - Bimatrix and polymatrix games are expressed as parametric linear 0-1 programs. This leads to an algorithm for the complete enumeration of their extreme equilibria, which is the first one proposed for polymatrix games. The algorithm computational experience is reported for two and three players on randomly generated games for sizes up to 14 x 14 and 13 x 13 x 13.

AB - Bimatrix and polymatrix games are expressed as parametric linear 0-1 programs. This leads to an algorithm for the complete enumeration of their extreme equilibria, which is the first one proposed for polymatrix games. The algorithm computational experience is reported for two and three players on randomly generated games for sizes up to 14 x 14 and 13 x 13 x 13.

KW - Bimatrix games

KW - Enumeration

KW - Extreme equilibria

KW - Nash equilibria

KW - Polymatrix games

UR - https://www.scopus.com/pages/publications/33845609599

U2 - 10.1007/s10957-006-9070-3

DO - 10.1007/s10957-006-9070-3

M3 - Article

AN - SCOPUS:33845609599

SN - 0022-3239

VL - 129

SP - 349

EP - 372

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Enumeration of all the extreme equilibria in game theory: Bimatrix and polymatrix games

Abstract

Keywords

ASJC Scopus subject areas

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