Mean field game for linear–quadratic stochastic recursive systems

Abstract

This paper focuses on linear–quadratic (LQ for short) mean-field games described by forward–backward stochastic differential equations (FBSDEs for short), in which the individual control region is postulated to be convex. The decentralized strategies and consistency condition are represented by a kind of coupled mean-field FBSDEs with projection operators. The well-posedness of consistency condition system is obtained using the monotonicity condition method. The ϵ-Nash equilibrium property is discussed as well.