Reputation with Noisy Precommitment

We investigate a game in which there is a long-run player who has private information about how long will the game last, who must precommit to an action, and who faces a sequence of short-run players who get a noisy signal of that action. We might expect such a long-lived long-run player to behave as a Stackelberg leader since most short-run players will eventually learn the true action. However, short-run players know that a long-run player that has been in the game for a long time must have chosen the Stackelberg action and may ignore the evidence from the signal. If so, the long-run player may have no reason to actually choose the Stackelberg action. We show that if there is a chance that the long-run player chooses other action by mistake, and the signal is sufficiently informative, this paradox can be resolved. We thank Michele Boldrin, Marco Celentani, and especially an Associate Editor for helpful comments and suggestions. Levine gratefully acknowledges support from the Spanish Ministry of Education DGICYT Grant SA95-0159, the UCLA Academic Senate, and National Science Foundation Grant SBR-93-20695. Martinelli gratefully acknowledges support from the Spanish Ministry of Education DGICYT Grant DD94-0378. Levine: Departments of Economics, UCLA, CA 90024; Martinelli: Departamento de Economía, Universidad Carlos III de Madrid, 28903 Getafe, Spain. This research was conducted while Levine was visiting at Carlos III.