2017/07/28 by Ahuja, Saran, Ren, Weiluo, Yang, Tzu-Wei
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1707.09090
In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose solution can be obtained through a coupled system of partial differential equations. We characterize the first order approximation via linear mean-field forward-backward stochastic differential equations whose solution is a centered Gaussian process with respect to the common noise. The first order approximate strategy can be described as follows: at time t ∈ [0,T], applying the original MFG optimal strategy for a sub game over [t,T] with the initial being the current state and distribution. We then show that this strategy gives an approximate Nash equilibrium of order ε2.