Decentralized Strategies for Backward Linear-Quadratic Mean Field Games and Teams

TL;DR

This paper introduces a novel class of linear-quadratic mean field games and teams involving weakly coupled backward stochastic differential equations, deriving explicit feedback strategies through Riccati equations and numerical simulations.

Contribution

It develops a new framework for mean field games with backward SDEs, providing explicit feedback strategies via Riccati equations and demonstrating the approach with numerical examples.

Findings

Derived a Hamiltonian system as a coupled FBSDE

Decoupled the system to obtain feedback strategies

Validated results with numerical simulation

Abstract

This paper studies a new class of linear-quadratic mean field games and teams problem, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equations (BSDEs), and $z_i$ (a part of solution of BSDE) enter the state equations and cost functionals. By virtue of stochastic maximum principle and optimal filter technique, we obtain a Hamiltonian system first, which is a fully coupled forward-backward stochastic differential equation (FBSDE). Decoupling the Hamiltonian system, we derive a feedback form optimal strategy by introducing Riccati equations, stochastic differential equation (SDE) and BSDE. Finally, we provide a numerical example to simulate our results.