Non-zero-sum stopping games in discrete time

TL;DR

This paper studies non-zero-sum stopping games in discrete time where players can adapt strategies based on each other's actions, establishing Nash equilibria in different strategic settings.

Contribution

It introduces a framework for non-zero-sum stopping games with sequential and simultaneous moves, proving the existence of Nash equilibria in mixed and pure strategies.

Findings

Existence of Nash equilibrium in mixed strategies for simultaneous moves

Existence of Nash equilibrium in pure strategies when one player acts first

Framework extends classical Dynkin game results to non-zero-sum settings

Abstract

We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game where players act simultaneously at each stage. We show that there exists a Nash equilibrium in mixed stopping strategies. In the second part, we assume that one player has to act first at each stage. In this case, we show the existence of a Nash equilibrium in pure stopping strategies.