Decentralized strategies for finite population linear–quadratic–Gaussian games and teams

This paper is concerned with a new class of mean-field games which involve finite number agents. Necessary and sufficient conditions are obtained for the existence decentralized open-loop Nash equilibrium in terms non-standard forward–backward stochastic differential equations (FBSDEs). By solving FBSDEs, we design set strategies by virtue two Riccati equations. Instead ɛ-Nash classical games, shown to be equilibrium. For infinite-horizon problem, simple condition given solvability algebraic equation arising from consensus. Furthermore, social optimal control problem studied. Under mild condition, corresponding cost given.