Nash equilibrium payoffs for non-zero-sum stochastic differential games without Isaacs condition

Abstract

ABSTRACTWe mainly investigate the existence of the Nash equilibrium payoffs for non-zero-sum stochastic differential games without assuming Isaacs condition in this paper. Along the partition π of the time interval , we choose a suitable random non-anticipative strategy with delay to study our non-zero-sum stochastic differential game. We prove for the corresponding both zero-sum stochastic differential games without Isaacs condition the existence of the value functions. With the help of these value functions we give the characterization of the Nash equilibrium payoffs. This characterization allows to prove the existence of Nash equilibrium payoffs.