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"Optimal Dynamic Information Acquisition" by Weijie Zhong
I study a dynamic model in which a decision maker (DM) acquires information about the payoffs of different alternatives prior to making her decision. The key feature of the model is the flexibility of information: the DM can choose any dynamic signal process as an information source, subject to a flow cost that depends on the informativeness of the signal. Under the optimal policy, the DM looks for a signal that arrives according to a Poisson process. The optimal Poisson signal confirms the DM’s prior belief and is sufficiently accurate to warrant an immediate action. Over time, absent the arrival of a Poisson signal, the DM continues seeking an increasingly more precise but less frequent Poisson signal.