Mean field LQG games with model uncertainty

This paper considers a class of mean field linear-quadratic-Gaussian (MFLQG) games. The system consists of a large number of negligible agents coupled through their cost functionals. Different to previous mean field game modeling, the stochastic differential equations of agents in our setup are subject to deterministic drift uncertainty satisfying an integral quadratic constraint. We deal with the model uncertainty by a robust optimization approach and formulate a minimax control problem in the infinite population limit. The state aggregation technique is applied where the mean field changes with the drift uncertainty which acts as an adversarial player. Based on the variational and Lagrange multiplier methods, a set of decentralized strategies is derived. The associated Hamiltonian system is represented by a system of coupled mean-field forward backward stochastic differential equations (FBSDEs) and some decoupling methods by Riccati equations are also presented.