Essays on Information Economics

Abstract

This dissertation is composed of three independent works in the field of Information Economics. Chapter 1 considers a Bayesian persuasion game in a new setting where a third party can endogenously choose to acquire outside information. I study how the precision of outside information or preferences of the signal-receivers can affect the timing to perform persuasion, which in turn affects the choice of optimal voting rule. Without incorporation of the new setting, unanimous rule is optimal while this result can break down under the new setting. Chapter 2 considers a collective decision problem in a setting where committee members have access to costly information of different precisions. I find that having all members who are all accessible to the most precise information does not result in the optimal design of the committee, and this chapter studies the conditions under which the optimal committee should include members who get access to less precise information. Chapter 3 studies Bayesian updating under uncertainty in the bias of public information. I find that more evidence supporting one opinion can possibly induce a Bayesian individual to be less convinced of that opinion. Also, when an information provider can improve the precision of his signals but this possibility is unknown to the information receivers, more precise information can result in a lower decision quality and a higher probability of polarization. Chapter 1: I study a persuasion game between a sender and a group of voters under the presence of an advisor who can access outside information to affect the collective decision. In addition to strategically designing a public signal, the sender can also affect the voters' information environment by choosing the timing of persuasion: either before (early) or after (late) the advisor makes his information acquisition decision. I provide sufficient and necessary conditions for a sender to strictly prefer early-persuasion. The main insight is that early-persuasion is adopted when the benefit of avoiding the leak of outside information exceeds the loss of sending over-informative signal. I then examine the optimal voting rules with and without outside information, and find that unanimity is no longer always optimal with outside information. Chapter 2: A group of members with identical preferences but heterogeneous abilities must make a collective decision under uncertainty about which decision is best. Before the decision is made, each member can acquire a costly and imperfect signal, and then members share with each other their signal results to reach an agreement on which alternative should be selected. I study how less accurate (weak) signals acquired by less efficient members (called inexperts) can contribute to the group's overall collection of information, and also derive the sufficient or necessary conditions for an optimal committee that should include positive number of inexperts. The insight behind the main results is that weak signals can help leverage the tradeoff between efficiently contributing to the group's overall collection of information and aggravating the free-rider problem among members. The main results are also robust to members having heterogeneous preferences, committee size being endogenous, or each signal becoming the provider's private information. Chapter 3: This paper studies a model in which Bayesian agents observe signals that are informative about the truth but are uncertain about the informativeness (not the direction) of each signal. As they observe additional signals, Bayesian updating requires that they not only learn about the truth but also update how they interpret the signals. Upon observing the same information, even though they interpret every single signal in the same direction, their attitudes toward the strength of evidence each signal represents can differ, and I provide the conditions under which this difference can result in polarization. When reputation refers to agents' beliefs that information is unbiased, I find that, by inducing a higher reputation, an information provider's choice of less precise information can possibly lead to a higher chance that agents make correct decisions and a lower probability that they polarize. Under mild assumptions, the main results are robust to agents having heterogeneous and biased prior beliefs in the truth.