# Mean Field Game for Linear Quadratic Stochastic Recursive Systems

## TL;DR

This paper develops a framework for linear-quadratic mean-field games involving forward-backward stochastic differential equations, establishing well-posedness and epsilon-Nash equilibrium properties for decentralized strategies.

## Contribution

It introduces a coupled mean-field FBSDE approach with projection operators for LQ mean-field games and proves well-posedness using monotonicity conditions.

## Key findings

- Established well-posedness of the consistency system.
- Proved epsilon-Nash equilibrium property.
- Provided a decentralized strategy framework.

## Abstract

This paper focuses on linear-quadratic (LQ for short) mean-field games described by forward-backward stochastic differential equations (FBSDEs for short), in which the individual control region is postulated to be convex. The decentralized strategies and consistency condition are represented by a kind of coupled mean-field FBSDEs with projection operators. The well-posedness of consistency condition system is obtained using the monotonicity condition method. The $\epsilon$-Nash equilibrium property is discussed as well.