Linear quadratic mean field game with control input constraint

Hu, Ying; Huang, Jianhui; Li, Xun

ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 901-919.

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 $\Gamma$ 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 $\Gamma$. The wellposedness of consistency condition system is obtained using the monotonicity condition method. The related $\in$-Nash equilibrium property is also verified.

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