Existence and stability of fuzzy Pareto-Nash equilibria for fuzzy constrained multi-objective games with fuzzy payoffs

Wen Li; Deyi Li; Yuqiang Feng; Du Zou; Wen Li; Deyi Li; Yuqiang Feng; Du Zou

doi:10.3934/math.2023812

AIMS Mathematics

2023, Volume 8, Issue 7: 15907-15931. doi: 10.3934/math.2023812

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Research article Special Issues

Existence and stability of fuzzy Pareto-Nash equilibria for fuzzy constrained multi-objective games with fuzzy payoffs

1.
School of Science, Wuhan University of Science and Technology, Wuhan 430065, China
2.
Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, China

Received: 03 January 2023 Revised: 09 April 2023 Accepted: 19 April 2023 Published: 04 May 2023
MSC : 91A10, 03E72, 37C20, 62G35

A new class of fuzzy constrained multi-objective games with fuzzy payoffs (FCMGFPs) is considered in this paper. First, Berge's maximum theorem for the fuzzy-vector-valued function is obtained. Based on this theorem and the Fan-Glicksberg fixed point theorem, the existence theorem of the fuzzy Pareto-Nash equilibrium for the FCMGFP is established. Second, the abstract rationality function for the FCMGFP is given by using a nonlinear scalarization function of interval vectors. Finally, a series of results, such as structural stability ($ (\gamma, \epsilon) $-stability) and robustness to $ \epsilon $-equilibrium ($ (\gamma, \epsilon) $-robustness), are obtained.
- fuzzy constrained multi-objective game,
- fuzzy payoff,
- fuzzy Pareto-Nash equilibrium,
- bounded rationality,
- structural stability,
- robustness
Citation: Wen Li, Deyi Li, Yuqiang Feng, Du Zou. Existence and stability of fuzzy Pareto-Nash equilibria for fuzzy constrained multi-objective games with fuzzy payoffs[J]. AIMS Mathematics, 2023, 8(7): 15907-15931. doi: 10.3934/math.2023812

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Abstract

A new class of fuzzy constrained multi-objective games with fuzzy payoffs (FCMGFPs) is considered in this paper. First, Berge's maximum theorem for the fuzzy-vector-valued function is obtained. Based on this theorem and the Fan-Glicksberg fixed point theorem, the existence theorem of the fuzzy Pareto-Nash equilibrium for the FCMGFP is established. Second, the abstract rationality function for the FCMGFP is given by using a nonlinear scalarization function of interval vectors. Finally, a series of results, such as structural stability ($ (\gamma, \epsilon) $-stability) and robustness to $ \epsilon $-equilibrium ($ (\gamma, \epsilon) $-robustness), are obtained.

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