On a Stopping Game in continuous time

TL;DR

This paper studies a novel zero-sum continuous-time stopping game where the payoff depends on the maximum of the two stopping times, contrasting with traditional Dynkin games that depend on the minimum.

Contribution

It introduces a new class of stopping games with payoffs based on the maximum of stopping times, expanding the theoretical framework of stopping games.

Findings

Characterization of the value of the game.

Existence of optimal stopping strategies.

Comparison with classical Dynkin games.

Abstract

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.