This was part of Mathematical Advances in Mean Field Games
Monotone solutions of the master equations
Charles Bertucci, Ecole Polytechnique
Wednesday, December 15, 2021
Abstract: This talk introduces a new notion of solutions for mean field games master equation. This notion relies on the monotonicity of the couplings and allows us to work with functions which are merely continuous in the measure argument. I will present results of existence, uniqueness and stability of those solutions, both in finite and continuous state space, as well as applications of this notion of solution to more singular mean field games like ones involving optimal stopping.