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 informationrevelation in equilibrium. This result is in sharp contrast to the famous Diamond paradox .
Consider a variation on the classic Weitzman search problem, in which competing firms can choose how much information about their product to reveal to a consumer . If there are no search frictions, there is a unique symmetric equilibrium in pure strategies; and for any market of finite size, the firms are not fully informative. With search frictions, if the expected value of the prize is sufficiently high, there is a unique symmetric equilibrium in which firms are fully informative . Remarkably, a small search cost leads to the perfect competition level of information provision : consumers gain when firms are forced to compete on information .
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competing
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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.
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finite number of firms, the signals
market of finite size, the firms
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If there are
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then
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unique
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pure strategies, but if it is too low, there is no such pure strategy equilibrium
which firms are fully informative
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it is always beneficial to the searcher to have a slight search cost: a
a
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Perfect Competition
perfect competition
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, but frictionless search leads to less informationrevelation in equilibrium. This result is in sharp contrast to the famous Diamond paradox
: consumers gain when firms are forced to compete on information