A new approach for solving constrained matrix games with fuzzy constraints and fuzzy payoffs

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Djebara Sabiha; Achemine Farida; Zerdani Ouiza

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Journal Paper

Paper Information

Journal: Journal of Mathematical Modeling Year:2023 | Volume:11 | Issue:3 Page(s): 425-439

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Title

A new approach for solving constrained matrix games with fuzzy constraints and fuzzy payoffs

Author(s)

Djebara Sabiha | Achemine Farida | Zerdani Ouiza | Issue Writer Certificate

Keywords

Chance-constraints

constrained matrix games

fuzzy games

Linear programming

saddle point equilibrium

Abstract

The main purpose of this study is to construct a new approach for solving a constrained matrix game where the payoffs and the constraints are LR-fuzzy numbers. The method that we propose here is based on chance constraints and on the concept of a comparison of fuzzy numbers. First, we formulate the fuzzy constraints of each player as chance constraints with respect to the possibility measure. According to a ranking function $\mathcal{R}$, a crisp constrained matrix game is obtained. Then, we introduce the concept of $\mathcal{R}$-saddle point equilibrium. Using results on ordering fuzzy numbers, sufficient existence conditions of this concept are provided. The problem of computing this solution is reduced to a pair of primal-dual linear programs. To illustrate the proposed method, an example of the market competition game is given.

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