Potential Competition in Preemption Games

Catherine Bobtcheff, and Thomas Mariotti


We consider a preemption game with two potential competitors who come into play at some random secret times. The presence of a competitor is revealed to a player only when the former moves, which terminates the game. We show that all perfect Bayesian equilibria give rise to the same distribution of players' moving times. Moreover, there exists a unique perfect Bayesian equilibrium in which each player's behavior from any time on is independent of the date at which she came into play. We find that competitive pressure is nonmonotonic over time, and that private information tends to alleviate rent dissipation. Our results have a natural interpretation in terms of eroding reputations.

JEL codes

  • C73: Stochastic and Dynamic Games • Evolutionary Games • Repeated Games
  • D82: Asymmetric and Private Information • Mechanism Design


Catherine Bobtcheff, and Thomas Mariotti, Potential Competition in Preemption Games, TSE Working Paper, n. 10-140, January 2010.

Published in

Games and Economic Behavior, vol. 75, n. 1, May 2012, pp. 53–66