This paper studies the reputation effect in which a long-lived player faces a sequence of uninformed short-lived players and the uninformed players receive informative but noisy exogenous signals about the type of the long-lived player.We provide an explicit lower bound on all Nash equilibrium payoffs of the longlived player. The lower bound shows when the exogenous signals are sufficiently noisy and the long-lived player is patient, he can be assured of a payoff strictly higher than his minmax payoff.
This article studies an information design problem in a sequential consumer search environment. Consumers, whose valuation of firms' products is uncertain, observe a noisy signal about the valuation upon being matched with a firm. The goal is to characterize those signal structures that maximize consumer surplus. We show that the consumer‐optimal signal structure can be found within the class of conditional unit‐elastic demand signal distributions. A rich set of properties and comparative statics of the consumer‐optimal signal distributions are also derived.
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