Wellposedness of Mean Field Games with Common Noise Under a Weak Monotonicity Condition

Understand

In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise.

• We assume a simple linear model with terminal cost satisfying a convexity and a weak monotonicity property.
• Our main result is showing existence and uniqueness of a Mean Field Game solution using the Stochastic Maximum Principle.
• The uniqueness is a result of a monotonicity property similar to that of Lasry and Lions.