On monotone solutions of mean field games master equations

Abstract

This note presents the concept of monotone solutions of mean field games master equations, in several cases. The first case that I treat is the one in which the underlying game has only a finite state space. The other are the case of a continuous state space and the so-called Hilbertian approach. Most of the results presented here come from the two papers [1, 2], except for results concerning the Hilbert space case and the case of general monotone operators which are new.