On existence of a Nash equilibrium point in N-person non-zero sum stochastic jump differential games

Abstract

Using the technique of Wan and Davis, we give an existence theorem for a Nash equilibrium point in N-person non-zero sum stochastic jump differential games. It is shown that if the Nash condition (generalized Isaacs condition) holds there is a Nash equilibrium point in feedback strategies. We extend the results to other solution concepts and discuss applications and extensions.