Fuzzy Weighted Pareto–Nash Equilibria of Multi-Objective Bi-Matrix Games with Fuzzy Payoffs and Their Applications

Based on our previous research, this paper further discusses the multi-objective bi-matrix game with fuzzy payoffs (MBGFP), which is a special case of the fuzzy constrained multi-objective game with fuzzy payoffs. We first prove that any bi-matrix game with interval payoffs (BGIP) has at least one P...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 20; p. 4266
Main Authors Li, Wen, Li, Deyi, Feng, Yuqiang, Zou, Du
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2023
Subjects
bi-matrix game with interval payoffs
bilinear programming model with parameters
Equilibrium
fuzzy payoffs
Fuzzy sets
fuzzy weighted Pareto–Nash equilibrium
Game theory
Games
Jargon
Linear programming
Mathematical analysis
multi-objective bi-matrix game
Multiple objective analysis
Iran
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Summary:Based on our previous research, this paper further discusses the multi-objective bi-matrix game with fuzzy payoffs (MBGFP), which is a special case of the fuzzy constrained multi-objective game with fuzzy payoffs. We first prove that any bi-matrix game with interval payoffs (BGIP) has at least one Pareto–Nash equilibrium. Then, with the help of BGIP, we obtain the necessary and sufficient conditions for the existence of fuzzy Pareto–Nash equilibrium of MBGFP. Secondly, based on the bilinear programming method for calculating Nash equilibrium in crisp bi-matrix games, we established a bilinear programming method with parameters for calculating fuzzy Pareto–Nash equilibrium. By considering the importance of each objective to the players, MBGFP is transformed into a bi-matrix game with fuzzy payoffs (BGFP). Furthermore, we obtained the necessary and sufficient conditions for the existence of fuzzy weighted Pareto–Nash equilibrium and its calculation method. Finally, a practical example is used to illustrate the effectiveness of our proposed calculation method.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11204266