Asymptotic Analysis of Mean Field Games with Small Common Noise

Understand

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 $t \in [0,T]$, applying the original MFG optimal strategy for a sub game over $[t,T]$ with the initial being the current state and distribution.