Potential competition in preemption games

We study a preemption game in which two potential competitors come into play at some random secret times. The presence of a competitor is revealed to her opponent only when the former moves, which terminates the game. We show that all perfect Bayesian equilibria give rise to the same distribution of playersʼ moving times, and we explicitly construct such an equilibrium. The intensity of competition is nonmonotonic over time, and private information tends to alleviate rent dissipation. Our results have a natural interpretation in terms of eroding reputations.