Proximal Calculus and Universal Feedback Strategies in Two Person Non-Zero Sum Differential Games

TL;DR

This paper introduces a discontinuous universal feedback approach for finding Nash equilibria in two-person non-zero sum differential games, expanding the theoretical framework beyond zero-sum scenarios.

Contribution

It establishes the existence of universal feedback Nash equilibrium under new assumptions analogous to zero-sum game conditions.

Findings

Proves existence of universal feedback Nash equilibrium.

Introduces discontinuous feedback strategies.

Extends differential game theory to non-zero sum cases.

Abstract

In this paper we introduce the discontinuous universal feedback for the problem of Nash equilibrium in two person non-zero sum differential game. We assume that there exist functions satisfying some conditions analogous to the infinitesimal conditions on value function in zero sum differential games. Under this assumption we prove the existence of universal feedback Nash equilibrium.