Monotone solutions for mean field games master equations : finite state space and optimal stopping

TL;DR

This paper introduces a new notion of continuous solutions for mean field games master equations in finite state spaces, proving uniqueness and stability, and applying it to optimal stopping and impulse control problems.

Contribution

It develops a novel solution concept for monotone mean field games master equations applicable to finite state spaces, with proofs of uniqueness and stability.

Findings

New solution notion for continuous solutions

Characterization of value functions in optimal stopping

Applicability to finite state space mean field games

Abstract

We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that this notion is helpful to characterize the value function of mean field games of optimal stopping or impulse control and this is the topic of the second half of this paper. The notion of solution we introduce is only useful in the monotone case. We focus in this paper in the finite state space case.