On Dynkin Games with Unordered Payoff Processes

TL;DR

This paper investigates Dynkin games with arbitrary payoff processes, establishing conditions for the existence of pure strategy Nash equilibria and epsilon-optimal stopping times in both discrete and continuous time settings.

Contribution

It generalizes the theory of Dynkin games by removing the usual ordering assumption on payoff processes, providing comprehensive equilibrium existence conditions.

Findings

Necessary and sufficient conditions for pure strategy Nash equilibria

Existence of epsilon-optimal stopping times in all subgames

Applicable to both discrete and continuous time frameworks

Abstract

A Dynkin game is a zero-sum, stochastic stopping game between two players where either player can stop the game at any time for an observable payoff. Typically the payoff process of the max-player is assumed to be smaller than the payoff process of the min-player, while the payoff process for simultaneous stopping is in between the two. In this paper, we study general Dynkin games whose payoff processes are in arbitrary positions. In both discrete and continuous time settings, we provide necessary and sufficient conditions for the existence of pure strategy Nash equilibria and epsilon-optimal stopping times in all possible subgames.