Information Provision in a Sequential Search Setting
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Consider a variation on the classic Weitzman search problem, in which firms can choose how much information about their product to reveal to a consumer who decides to search them. In this zero-sum game, ex-ante identical firms commit to a signal distribution as a function of quality before they learn their (random) quality; a firm's goal is to maximize the chance that its product is the one selected by the searcher. If there are no search frictions, there is a unique symmetric equilibrium in pure strategies; and for any finite number of firms, the signals are not fully informative. If there are search frictions, then if the expected value of the prize is sufficiently high, there is a symmetric equilibrium in pure strategies, but if it is too low, there is no such pure strategy equilibrium. Remarkably, it is always beneficial to the searcher to have a slight search cost: a small search cost leads to the Perfect Competition level of information provision, but frictionless search leads to less information revelation in equilibrium. This result is in sharp contrast to the famous Diamond paradox.
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