Existence and generic stability of open-loop Nash equilibria for noncooperative fuzzy differential games

Abstract

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 Γ1 is constructed, and the stability of open-loop Nash equilibria of the fuzzy differential game γ∈Γ1 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.