Optimal Dynamic Information Acquisition

In this paper, I studied an information acquisition problem: a decision maker acquires information about payoff relevant states to facilitate decision making. My primary focus is on flexibility: the decision maker can choose any dynamic signal process as information source, subject to cost on signal informativeness in unit time. I fully characterized optimal learning dynamics with posterior separable informativeness measure: the decision maker will seek for an informative evidence arriving as a Poisson process which Confirms prior belief and lead to Immediate action . Learning has Increasing precision and Decreasing intensity over time. Moreover, I showed that the learning dynamics has a proper discrete time foundation and optimality of Poisson is robust to general informativeness measure