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

Abstract

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 $e$−Nash equilibrium property is also verified.