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

Wen Li, Deyi Li, Yuqiang Feng () and Du Zou
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Wen Li: School of Science, Wuhan University of Science and Technology, Wuhan 430065, China
Deyi Li: School of Science, Wuhan University of Science and Technology, Wuhan 430065, China
Yuqiang Feng: School of Science, Wuhan University of Science and Technology, Wuhan 430065, China
Du Zou: School of Science, Wuhan University of Science and Technology, Wuhan 430065, China

Mathematics, 2023, vol. 11, issue 20, 1-18

Abstract: 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.

Keywords: multi-objective bi-matrix game; fuzzy payoffs; fuzzy weighted Pareto–Nash equilibrium; bi-matrix game with interval payoffs; bilinear programming model with parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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