Perpetual signaling with imperfectly correlated costs
In many imperfect-information models in industrial organization, a firm is induced to take an action that does not maximize its first-period profit because other firms view this action as a signal about the firm's private information. In these models, because the opponent firms can correctly invert the firm's strategy, all information is revealed after play in the first period, and in subsequent periods all firms play their single-period profit-maximizing strategies. Thus, behavior like limit pricing is observed only in the first period, and not in any subsequent period. The empirical importance of such signalling behavior, however, depends on its being perpetuated through time rather than being a single-period phenomenon. In this article, such perpetual signalling is obtained by allowing the variable about which firms have private information to vary through time. In a separating equilibrium, while a firm's action will perfectly reveal its private information in a period, it will not perfectly reveal the firm's private information in subsequent periods. Thus, the incentive to signal perpetuates through time.
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