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 in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets ${\Gamma }_k$ of ${\mathbb{R}}^m.$ The decentralized strategies for individual agents and consistency condition system are represented in an unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on ${\Gamma }_k$. The well-posedness of consistency system is established in both the local and global cases by the contraction mapping and discounting method respectively. Related $\epsilon -$Nash equilibrium property is also verified.

40 pages

References in corpus (1)

• Linear Quadratic Mean Field Game with Control Input Constraint

Cited by in corpus (1)

• Linear-Quadratic Mixed Stackelberg-Nash Stochastic Differential Game with Major-Minor Agents