Zero-sum mean-field Dynkin games: characterization and convergence

TL;DR

This paper extends classical zero-sum Dynkin games to a mean-field setting where payoffs depend on the game value and its distribution, establishing existence, characterization, and convergence results.

Contribution

It introduces a mean-field zero-sum Dynkin game framework, characterizes its value via mean-field doubly reflected BSDEs, and proves convergence of the interacting game system.

Findings

Existence of a game value and saddle point under certain conditions

Characterization of the value through mean-field doubly reflected BSDEs

Propagation of chaos for the game value

Abstract

We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish sufficient conditions under which such a game admits a value and a saddle point. Furthermore, we provide a characterization of the value of the game in terms of a specific class of doubly reflected backward stochastic differential equations (BSDEs) of mean-field type, for which we derive an existence and uniqueness result. We then introduce a corresponding system of weakly interacting zero-sum Dynkin games and show its well-posedness. Finally, we provide a propagation of chaos result for the value of the zero-sum mean-field Dynkin game.