A note on bimatrix game maximal Selten subsets

Slim Belhaiza; Charles Audet; Pierre Hansen

doi:10.1007/s40065-014-0101-x

A note on bimatrix game maximal Selten subsets

Slim Belhaiza^*, Charles Audet, Pierre Hansen

^*Corresponding author for this work

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

Abstract

In this paper, we implement automatic procedures to enumerate all Nash maximal subsets of a bimatrix game and compute their dimensions. We propose a linear programming approach to identify extreme perfect Nash equilibria, enumerate all Selten maximal subsets and compute their dimensions. We present the Eχ-MIPerfect and the EEE-Perfect algorithms which enumerate all extreme perfect Nash equilibria. We finally report and comment computational experiments on randomly generated bimatrix games with different size and density. [Figure not available: see fulltext.]

Original language	English
Pages (from-to)	299-311
Number of pages	13
Journal	Arabian Journal of Mathematics
Volume	3
Issue number	3
DOIs	https://doi.org/10.1007/s40065-014-0101-x
State	Published - 1 Sep 2014

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Publisher Copyright:
© 2014, The Author(s).

ASJC Scopus subject areas

General Mathematics

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10.1007/s40065-014-0101-x

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N2 - In this paper, we implement automatic procedures to enumerate all Nash maximal subsets of a bimatrix game and compute their dimensions. We propose a linear programming approach to identify extreme perfect Nash equilibria, enumerate all Selten maximal subsets and compute their dimensions. We present the Eχ-MIPerfect and the EEE-Perfect algorithms which enumerate all extreme perfect Nash equilibria. We finally report and comment computational experiments on randomly generated bimatrix games with different size and density. [Figure not available: see fulltext.]

AB - In this paper, we implement automatic procedures to enumerate all Nash maximal subsets of a bimatrix game and compute their dimensions. We propose a linear programming approach to identify extreme perfect Nash equilibria, enumerate all Selten maximal subsets and compute their dimensions. We present the Eχ-MIPerfect and the EEE-Perfect algorithms which enumerate all extreme perfect Nash equilibria. We finally report and comment computational experiments on randomly generated bimatrix games with different size and density. [Figure not available: see fulltext.]

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A note on bimatrix game maximal Selten subsets

Abstract

Bibliographical note

ASJC Scopus subject areas

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