Published in Journal of Economic Theory, 78: 55-75, 1998
David K. Levine and Cesar Martinelli
revised: August 13, 1997
Abstract: 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.