Existence and generic stability of open-loop Nash equilibria for noncooperative fuzzy differential games. (English) Zbl 07764801
Summary: Differential game is a critical area of study not only in theory but also in application. Based on the concept of the fuzzy process introduced by Liu, a fuzzy differential game model described using fuzzy differential equations is studied. Firstly, the existence theorem of open-loop Nash equilibrium for fuzzy differential games is given using Ky Fan inequality, and an example shows the applicability of the theorem. Secondly, the fuzzy differential game space \(\Gamma_1\) is constructed, and the stability of open-loop Nash equilibria of the fuzzy differential game \(\gamma \in \Gamma_1\) is studied. The conclusion shows that the fuzzy differential games whose all the open-loop Nash equilibria are stable form a dense residual set, i.e., most of the fuzzy differential games are stable in the sense of Baire classification.
Keywords:
open-loop Nash equilibrium; fuzzy differential games; generic stability; set-valued mappingReferences:
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