Essays on information acquisition

This dissertation studies information acquisition when the choice of information is fully flexible. Throughout the dissertation, I consider a theoretical framework where a decision maker (DM) acquires costly information (signal process) about the payoffs of different alternatives before making a choice. In Chapter 1, I solve a general model where the DM pays a cost that depends on the rate of uncertainty reduction and discounts delayed payoffs. The main finding is that the optimal signal process resembles a Poisson signal --- the signal arrives occasionally according to a Poisson process, and it drives the inferred posterior belief to jump discretely. The optimal signal is chosen to confirm the DM's prior belief of the most promising state. Once seeing the signal, the decision maker is discretely surer about the state and stops learning immediately. When the signal is otherwise absent, the decision maker becomes gradually less sure about the state, and continues learning by seeking more precise but less frequently arriving signals. In Chapter 2, I study the sequential implementation of a target information structure. I characterize the set of decision time distributions induced by all signal processes that satisfy a per-period learning capacity constraint on the rate of uncertainty reduction. I find that all decision time distributions have the same mean, and the maximal and minimal elements by mean-preserving spread order are exponential distribution and deterministic distribution. The result implies that when the time preference is risk loving (e.g. standard or hyperbolic discounting), Poisson signal is optimal since it induces the riskiest exponential decision time distribution. When time preference is risk neutral (e.g. constant delay cost), all signal processes are equally optimal. In Chapter 3, I relax the assumption on information cost by assuming that the measure of signal informativeness is an indirect measure from sequential minimization. I first show that an indirect information measure is supported by sequential minimization iff it satisfies: 1) monotonicity in Blackwell order, 2) sub-additivity in compound experiments and 3) linearity in mixing with no information. Then I study a dynamic information acquisition problem where the cost of information depends on an indirect information measure and the delay cost is fixed (the DM is time-risk neutral). The optimal strategy is to acquire Poisson type signals. The result implies that when the cost of information is measured by an indirect measure, Poisson signals are intrinsically cheaper than other signal processes. Chapter 4 introduces a set of useful technical results on constrained information design that is used to derive the main results in the first three chapters.