Multi-Player Stopping Games in Continuous Time

Abstract

We consider multi-player stopping games in continuous time. Unlike Dynkin games, in our games the payoff of each player is revealed after all the players stop. Moreover, each player can adjust her own stopping strategy by observing other players’ behaviors. Assuming the continuity of the payoff functions in time, we show that there always exists an ε-Nash equilibrium in pure stopping strategies for any ε > 0. Our game has a wide range of applications, e.g., when companies choose times to take actions, and e.g., when investors who both short and long American options try to maximize their utilities.

Keywords: Multi-player, stopping games, Nash equilibrium.