Mean field games with common noise

Abstract

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

References in corpus (2)

• Mean field games via controlled martingale problems: Existence of Markovian equilibria
• The Master Equation in Mean Field Theory

Cited by in corpus (3)

• Mean field games via controlled martingale problems: Existence of Markovian equilibria
• A general characterization of the mean field limit for stochastic differential games
• Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource