Robust Mean Field Games

Recently there has been renewed interest in large-scale games in several research disciplines, with diverse application domains as in the smart grid, cloud computing, nancial markets, biochemical reaction networks, transportation science and molecular biology. Prior works have provided rich mathematical foundations and equilibrium concepts but relatively little in terms of robustness in the presence of uncertainties. In this paper, we study mean-eld games with uncertainty in both states and payos. We consider a population of players with individual states driven by a standard Brownian motion and a disturbance term. The contribution is three-fold: First, we establish a mean eld system for such robust games. Second, we apply the methodology to production of an exhaustible resource. Third, we show that the dimension of the mean eld system can be signicantly reduced by considering a functional of the first moment of the mean field process.