Abstract
We introduce the concept of master field within the framework of mean field games with a common noise. We present it as the decoupling field of an infinite dimensional forward-backward system of stochastic partial differential equations characterizing the equilibria. The forward equation is a stochastic Fokker-Planck equation and the backward equation a stochastic Hamilton-Jacobi-Bellman equation. We show that whenever existence and uniqueness of equilibria hold for any initial condition, the master field is a viscosity solution of Lions’ master equation.
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