On Existence of a Nash Equilibrium Point in N-Person Nonzero Sum Stochastic Differential Games

Using the technique of Davis and Varaiya, we give an existence theorem for a Nash equilibrium point in N-person nonzero sum stochastic differential games. It is shown that if the Nash condition (generalized Isaacs condition) holds there is a Nash equilibrium point in feedback strategies. Also we discuss two special cases where the Nash condition holds.