Title: Essays in Information Economics and Monotone Comparative Statics
Description: This dissertation studies communication in a variety of contexts and attempts to derive general comparative statics results and equilibrium characterizations. The main goal is to understand how usual comparative statics predictions extend to realistic but previously intractable frameworks. These range from examining communication when outcomes are lotteries, to disclosure games when the evidence structure can be arbitrarily complex. Chapter 1 studies verifiable disclosure games, that is, a sender communicating with a receiver using hard evidence in order to influence his action choice. The main goal is to understand how prior beliefs about the evidence environment affect which actions are chosen in equilibrium. More specifically, the goal is to understand which beliefs will be less preferred by the sender: I say that a prior belief is more skeptical than another if it induces less preferred equilibrium actions for the sender regardless of his type or the receiver's preferences. The main contribution is to show that this equilibrium order, which is difficult to check. is equivalent to when the sender is expected to have more evidence, a more straightforward order over the primitives.

This equivalence has application to any disclosure game in which the sender can affect or choose the receiver that he faces. Examples include jury selection and dynamic disclosure. In addition, the methodology of the paper provides an explicit expression for equilibrium actions, and a novel comparative statics result. Chapter 2 studies when choice over lotteries is monotonic given any choice set. A central prediction of the signaling literature is monotone comparative statics (MCS) or that higher types choose higher outcomes. The driving behavioral assumption behind MCS is the single crossing property on preferences. However, this property is only sufficient when the outcome is non-random. More realistically, choices correspond to lotteries over outcomes: a student choosing her education level is not certain about her lifetime salary. Motivated by this observation we characterize preferences that admit an analogous single crossing property over lotteries. We show that this property is necessary and sufficient to maintain MCS in many signaling applications when noise is introduced after the choice has been made.

Chapter 3 studies how a principal incentivizes costly information acquisition from a disinterested agent through monetary transfers. The main focus is the moral hazard that arises when the principal can observe the results of the investigation but not the entire research process. More specifically, we assume that the principal can contract on the realized posterior belief but not on the posterior beliefs that could have been realized or on their probability. We find that, unlike in standard moral hazard problems, under either limited liability or risk aversion the principal implements his first best experiment at first best cost. However, under risk aversion and limited liability the principal suffers efficiency loss. More specifically, if the principal plans to implement an asymmetric experiment, one which seeks certainty with low probability and is uninformative otherwise, the second best experiment will be distorted toward less asymmetric experiments and provide the agent with a positive rent.