Monotone solutions for mean field games master equations: continuous state space and common noise

Abstract

AbstractWe present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows us to work with solutions which are merely continuous in the measure argument, in the case of first order master equations. We study several structures of common noises, in particular ones in which common jumps (or aggregate shocks) can happen randomly, and ones in which the correlation of randomness is carried by an additional parameter.KEYWORDS: Mean Field GamesMaster equationWeak solutions Notes1 C−k is the topological dual set of C k while we understand C1,1 in the sense that the usual differential is a Lipschitz function.