Mean-Field Games with Common Noise Based on Nonlinear Diffusion Processes

摘要

The aim of the paper is to study of the mean field games with common noise. The MFG limit is specified by a single quasi-linear deterministic infinite-dimensional partial differential second order backward equation. We show that any its solution provides an 1/N-Nash equilibrium for the initial game of N agents. Our basic approach is based on interpreting the common noise as a kind of binary interaction of agents and then reducing the problem to the sensitivity analysis for McKean-Vlasov SPDE.