Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-Disturbance

TL;DR

This paper develops a robust solution framework for mean field LQG games with unknown drift disturbances, employing a game-theoretic approach and FBSDEs to achieve epsilon-Nash equilibria under model uncertainty.

Contribution

It introduces a novel robust control methodology for mean field LQG games with unknown drift, utilizing an augmented state space and sequential control problems.

Findings

Derives decentralized control strategies using FBSDEs.

Establishes the existence of robust epsilon-Nash equilibria.

Provides a systematic approach to handle model uncertainty in mean field games.

Abstract

This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a representative agent in the limiting model views the drift uncertainty as an adversarial player. By including the mean field dynamics in an augmented state space, we solve two optimal control problems sequentially, which combined with consistent mean field approximations provides a solution to the robust game. A set of decentralized control strategies is derived by use of forward-backward stochastic differential equations (FBSDE) and shown to be a robust epsilon-Nash equilibrium.