Linear quadratic mean field game with control input constraint

Abstract

In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset F of full space R-m. The decentralized strategies and consistency condition are represented by a class of mean-field forward-backward stochastic differential equation (MF-FBSDE) with projection operators on F. The wellposedness of consistency condition system is obtained using the monotonicity condition method. The related is an element of-Nash equilibrium property is also verified.