Linear Quadratic Mean Field Game with Control Input Constraint

Ying Hu (1) , Huang Jianhui (2) , Xun Li (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 POLYU - The Hong Kong Polytechnic University [Hong Kong]

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 Γ 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 Γ. The wellposedness of consistency condition system is obtained using the monotonicity condition method. The related ǫ-Nash equilibrium property is also verified.

Mots clés: ǫ-Nash equilibrium; Mean-field forward-backward stochastic differential equa-; tion (MF-FBSDE); Linear-quadratic constrained control; Projection; Monotonic condition; AMS Subject Classification: 93E20; 60H10

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Ying Hu, Huang Jianhui, Xun Li. Linear Quadratic Mean Field Game with Control Input Constraint. ESAIM: Control, Optimisation and Calculus of Variations, 2018, 24 (2), pp.901 - 919. ⟨10.1051/cocv/2017038⟩. ⟨hal-01383611⟩