Non-Zero-Sum Stopping Games in Discrete Time

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. Our results have a lot of applications, e.g., when companies choose times to enter the market, or when investors who both long and short American options choose times to exercise the options.