On the Set of Equilibria of a Bimatrix Game: a Survey

The article examines the behavior of students and employers as a bimatrix game. With the tools of game theory, it is generally proven that the optimal strategy for employers is to pay low wages, and for students – not to study or to study too little. These two strategies form the Nash’s equilibrium in pure strategies. No specific numbers were used in the evidence, but only plausible assumptions about the relationships between the used parameters. This generalizes the conclusions made in the general case of higher education. Such a study of the question using game theory has not been done yet.

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On Solving Bilevel Optimization Problems with a Nonconvex Lower Level: The Case of a Bimatrix Game

Mathematical Optimization Theory and Operations Research - Lecture Notes in Computer Science ◽

10.1007/978-3-030-77876-7_16 ◽

2021 ◽

pp. 235-249

Author(s):

A. V. Orlov

Keyword(s):

Optimization Problems ◽

Bilevel Optimization ◽

Bimatrix Game

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Evolutionary Game Model of 2 × 2 Stochastic Bimatrix Game based on Quasi Birth and Death Process

Systems Engineering - Theory & Practice ◽

10.1016/s1874-8651(08)60024-1 ◽

2007 ◽

Vol 27 (3) ◽

pp. 56-62

Author(s):

Qian YU ◽

Xian-jia WANG

Keyword(s):

Evolutionary Game ◽

Death Process ◽

Game Model ◽

Birth And Death Process ◽

Bimatrix Game

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Support Set Invariancy for Interval Bimatrix Games

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488519500107 ◽

2019 ◽

Vol 27 (02) ◽

pp. 225-237

Author(s):

Milan Hladík

Keyword(s):

Mixed Integer ◽

Necessary Condition ◽

Linear Programs ◽

Bimatrix Games ◽

Bimatrix Game ◽

Integer Programs ◽

Mixed Integer Programs ◽

Support Set ◽

First Case ◽

Pure Strategies

Traditionally, game theory problems were considered for exact data, and the decisions were based on known payoffs. However, this assumption is rarely true in practice. Uncertainty in measurements and imprecise information must be taken into account. The interval-based approach for handling such uncertainties assumes that one has lower and upper bounds on payoffs. In this paper, interval bimatrix games are studied. Especially, we focus on three kinds of support set invariancy. Support of a mixed strategy consists of that pure strategies having positive probabilities. Given an interval-valued bimatrix game and supports for both players, the question states as follows: Does every bimatrix game instance have an equilibrium with the prescribed support? The other two kinds of invariancies are slight modifications: Has every bimatrix game instance an equilibrium being a subset/superset of the prescribed support? It is computationally difficult to answer these questions: the first case costs solving a large number of linear programs or mixed integer programs. For the remaining two cases a sufficient condition and a necessary condition are proposed, respectively.

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