A sufficient condition for decentralized non-cooperative stochastic differential games and relations to mean field games

In this paper we use martingale techniques to derive a sufficient condition for existence of decentralized strategies in non-cooperative stochastic differential games. The sufficient condition is given by decentralized conditional Isaacs conditions, linked to backward stochastic differential equations, whose solutions are related to the value processes of each one of the Decision Makers (DMs) or Players of the game. Our formulation and results include decentralized noncooperative stochastic games with mean field and conditional mean field components.