A Competitive Optimal Stopping Game

摘要

This paper explores a multi-player game of optimal stopping over a finite time horizon. A player wins by retainingrna higher value than her competitors do, from a series of independent draws. In our game, a cutoff strategy isrnoptimal, we derive its form, and we show that there is a unique Bayesian Nash Equilibrium in symmetric cutoffrnstrategies. We establish results concerning the cutoff value in its limit and expose techniques, in particular, usernof the Budan-Fourier Theorem, that may be useful in other similar problems.