Reputation with Noisy Precommitment

David K. Levine
Cesar Martinelli

Abstract

A long-run player, with private information about how long the game will last, must precommit to an action and faces a sequence of short-run players who get a noisy signal of that action. Since noise vanishes with time, we might expect a long-lived long-run player to behave as a Stackelberg leader. If so, short-run players may end up ignoring the signal. Then, however, the long-run player would have no reason to actually choose the Stackelberg action. We show that this paradox can be resolved if there is a chance that the long-run player chooses other action by mistake, and the signal is sufficiently informative.