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

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...

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Published inAIMS mathematics Vol. 8; no. 7; pp. 15907 - 15931
Main Authors Li, Wen, Li, Deyi, Feng, Yuqiang, Zou, Du
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
bounded rationality
fuzzy constrained multi-objective game
fuzzy pareto-nash equilibrium
fuzzy payoff
robustness
structural stability
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023812