A mean field LQG game with soft-constrained disturbance as an adversarial player

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 incorporating the temporal evolution of the mean field in an augmented state space, we solve two optimal control problems sequentially subject to a consistency requirement for the mean field approximation. A set of decentralized control strategies is obtained as a robust ε-Nash equilibrium.