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

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.

Keywords

• fuzzy constrained multi-objective game
• fuzzy payoff
• fuzzy pareto-nash equilibrium
• bounded rationality
• structural stability
• robustness