Linear-Quadratic-Gaussian Mixed Mean-field Games with Heterogenous 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 Heterogenous Input Constraints. 2017. ⟨hal-01590971v1⟩