| In a decision problem under uncertainty, the decision maker gathers information about payoff-relevant variables from a set of possible signals. The first chapter deals with definitions in which one signal can be judged to be better than another, and proposes four distinct approaches to formulating a partial ordering on the set of signals. Under the statistical and Bayesian frameworks, I provide the respective ways to arrange signals by value---based on the criterion of effectiveness and informativeness---and illustrate why each criterion induces a reasonable signal ordering. In addition, I provide another two ways to rank signals by statistical property---based on Lehmann precision and dispersion---with an emphasis on their relationship.;The second chapter presents the major result of the dissertation. I show that the four different signal orderings presented in Chapter 1 are mutually equivalent within each of three classes of payoff functions: supermodular, single-crossing, and interval dominance order. Subsequently, I discuss two important implications of this equivalence theorem. First, Lehmann precision is both necessary and sufficient for one signal to be more valuable than another to both statisticians and Bayesian decision makers. Second, the theorem exactly characterizes the relationship between more precise signals and higher dispersion by coupling the precision-based ordering with the dispersion-based ordering. This result---called the dispersion theorem---justifies another signal orderings used in the previous literature.;In the third chapter I use the dispersion theorem to examine the impact of precise information in several economic environments with strategic interactions. The first application is to auctions. I investigate how the seller's activity of supplying precise information to bidders impinges on efficiency, the expected revenue, and the bidder's information rent. The second is to the principal-agent model with hidden action. I show that a more precise contractible variable is necessary and sufficient for the principal to be able to control the agent's hidden action with less cost. The third is to delegation. I provide a sufficient condition for the value of delegation to be monotonic in the level of agent's expertise. |
