On the set of proper equilibria of a bimatrix game
type: Item
instance of: scholarly article
title: On the set of proper equilibria of a bimatrix game
zbMATH Open document ID: 0797.90121
DOI: 10.1007/BF01243644
author: Mathijs Jansen
published in: International Journal of Game Theory
publication date: 1993-12-20T00:00:00Z
review text: The paper is devoted to the analysis of the set of proper equilibria of a bimatrix game. It discusses the well-known problem which started from the structure of the set of Nash equilibria of a matrix game. This set is the Cartesian product of two polytopes in the case of a matrix game. The main result of this paper is that the set of proper equilibria of a bimatrix game is the finite union of polytopes. The mathematical technique for proving this result is based on the representation of the set of strategies (the strategy space) of each player into a finite number of equivalence classes. A Myerson set of proper equilibria is considered. The main results are the following: Theorem 1. The set of proper equilibria of a bimatrix game is the union of a finite number of polytopes. Theorem 2. The intersection of two maximal Myerson sets is empty on a face of both maximal sets.
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 429105
zbMATH Keywords: set of proper equilibria
zbMATH Keywords: bimatrix game
zbMATH Keywords: finite union of polytopes
zbMATH Keywords: Myerson set
reviewed by: Andreiy Kondrat'yev
MaRDI profile type: Publication
cites work: Pareto equilibria for bimatrix games
cites work: Q5801628
cites work: Refinements of the Nash equilibrium concept
cites work: Q5801627
cites work: On nash subsets and mobility chains in bimatrix games
cites work: Maximal nash subsets for bimatrix games
cites work: Equilibrium points in n -person games
cites work: The Nucleolus of a Matrix Game and Other Nucleoli
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full work available at URL: https://doi.org/10.1007/bf01243644
OpenAlex ID: W1994988191
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description: scientific article; zbMATH DE number 429105