Stability of open-loop Nash equilibria for n-person nonzero-sum bounded rationality generalized differential games

Abstract

The problem of determining the existence of Nash equilibria in $n$-person nonzero-sum generalized differential games is highly intricate and constrained by the advancement of partial differential equations theory. There is limited existing research literature on this subject. This paper presents an existence theorem for open-loop Nash equilibria employing the Fan-Glicksberg fixed point theorem. The $n$-person nonzero-sum bounded rationality generalized differential game model is formulated by introducing a bounded rationality function, and its structural stability and robustness are studied. The conclusions indicate that in the sense of Baire classification, most $n$-person nonzero-sum bounded rationality generalized differential games are structurally stable and robust in the set of $\varepsilon$-open-loop Nash equilibria, and we can approximate the equilibrium set obtained with full rationality generalized differential games by the ${\varepsilon }^k$-open-loop Nash equilibria set obtained with bounded rationality generalized differential games.