Mean-field games of optimal stopping: master equation and weak equilibria

TL;DR

This paper studies mean-field games involving optimal stopping, establishing the existence of equilibria, their approximation for finite-player games, and deriving the associated master equation.

Contribution

It introduces a weak formulation for mean-field optimal stopping games, proving equilibrium existence and linking mean-field solutions to finite-player Nash equilibria.

Findings

Existence of Nash equilibria in the weak formulation.

Mean-field equilibria approximate finite-player Nash equilibria.

Derivation of the master equation for the mean-field game.

Abstract

We are interested in the study of stochastic games for which each player faces an optimal stopping problem. In our setting, the players may interact through the criterion to optimise as well as through their dynamics. After briefly discussing the N-player game, we formulate the corresponding mean-field problem. In particular, we introduce a weak formulation of the game for which we are able to prove existence of Nash equilibria for a large class of criteria. We also prove that equilibria for the mean-field problem provide approximated Nash equilibria for the N-player game, and we formally derive the master equation associated with our mean-field game.