Mean field games with common noise

Abstract

A theory of existence and uniqueness is developed for general stochastic diferential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic diferential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counterexamples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and Watanabe is derived, and used to prove existence and uniqueness of a strong solution under additional assumptions.