We study a class of optimal stopping games (Dynkin games) of preemption type, with uncertainty about the existence of competitors. The set-up is well-suited to model, for example, real options in the context of investors who do not want to publicly reveal their interest in a certain business opportunity. We show that there exists a Nash equilibrium in randomized stopping times which is described explicitly in terms of the corresponding one-player game.

中文翻译：

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在 Dynkin 游戏中玩鬼

我们研究了一类具有竞争者存在不确定性的抢占型最优停止博弈（Dynkin 博弈）。该设置非常适合模拟实物期权，例如，投资者不想公开透露他们对某个商业机会的兴趣。我们表明在随机停止时间中存在纳什均衡，这在相应的单人游戏中被明确描述。