Linear-Quadratic-Gaussian Mixed Mean-field Games with Heterogeneous Input Constraints

Ying Hu (1) , Jianhui Huang (2) , Tianyang Nie (3)

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

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents with mean-field interactions. The individual admissible controls are constrained in closed convex subsets $Γ k$ of full space $R m$. The decentralized strategies for individual agents and consistency condition system are represented in an unified manner via a class of mean-field forward-backward stochastic differential equations involving projection operators on $Γ k$. The well-posedness of consistency system is established in the local and global cases both by the contraction mapping and discounting method respectively. The related $ε$−Nash equilibrium property is also verified.

Mots clés: $ε$-Nash equilibrium; Forward-backward stochastic differential equation; Input constraint; Projection operator; Linear-quadratic mixed mean-field games

Domaines: Optimisation et contrôle [math.OC]

Ying Hu, Jianhui Huang, Tianyang Nie. Linear-Quadratic-Gaussian Mixed Mean-field Games with Heterogeneous Input Constraints. SIAM Journal on Control and Optimization, 2018, 56 (4), pp.2835-2877. ⟨10.1137/17M1151420⟩. ⟨hal-01590971v2⟩