Essays on Information Economics

Abstract

Each person has his aspiration and fear in the face of the prevailing uncertainty about the state of the world. Uncertainty obscures the potential consequences of taking certain actions and makes decision makers hesitate. A consumer would hesitate to try a new product when its quality is still an unknown. An investor would hesitate to buy in or sell off confronting volatile stock prices. A judge would hesitate to make her decisions on a lawsuit case with partial evidence at hand. In the presence of uncertainty, a demand for information arises from these economic settings. To some extent, information transmission can be viewed as a certain type of ``trade,'' where an agent releases information in exchange for more favorable actions the information would influence other agents to take. That being said, an informed party or a party who has the ability to acquire information can withhold information in his best interest. To address the effect of conflicts of interest on information revelation gives rise to the literature of communication games, which is the area this dissertation belongs to. This line of literature consists of three main models: cheap talk, disclosure, and Bayesian persuasion. In cheap talk, an informed party sends a plain message to an uninformed party; In disclosure, besides plain messages, the informed party can also present hard evidence; In Bayesian persuasion, however, one party publicly acquires information through a determined scheme. My dissertation builds on and contributes to these models. There are three chapters with different focuses. Below I will briefly summarize the contents of each chapter. In Chapter 1, I study a Bayesian persuasion model in which multiple senders sequentially persuade one receiver after observing signaling rules of prior senders and their realizations. I develop a novel method, recursive concavification, to characterize the Subgame Perfect Equilibrium paths. I show that if there are two senders who have constant-sum payoffs, the truth-telling information structure is always supported in equilibrium. I prove the existence of the silent equilibrium, where at most one sender designs a nontrivial signaling rule. I also provide sufficient conditions under which it is without loss of generality to focus on silent equilibria. In Chapter 2 (joint work with Bohan Ye), we experimentally investigate a classic question, whether competition stimulates information revelation, by comparing two Bayesian persuasion models, one with one sender (Kamenica and Gentzkow, 2011) and the other with two competing senders who move sequentially (Wu, 2018). The first experiment provides strong support for Kamenica and Gentzkow (2011), where the sender uses a vague signaling device and the receiver complies with his suggestions. In the second experiment, we find that (1) more information is revealed than in the first experiment; (2) the first sender reduces the use of the vague device as compared to the single sender in the first experiment; (3) the second sender exhibits a ``matching'' behavior pattern; (4) the receiver can make use of information from both sides. However, our experiments also document deviation from the theory. Competition does not improve information revelation to the extent of full information, as predicted by theory. To rationalize the behavior, we use the Quantal Response Equilibrium model to explain the features of the empirical results in our experiments. In Chapter 3, I study a one-sender-one-receiver disclosure game with general receiver preferences and message structures. Drawing on techniques from information design, I provide a characterization of the Perfect Bayesian Equilibrium outcomes. I find that any PBE can be interpreted as a combination of cheap talk equilibria in a partitional form. I revisit Milgrom (1981, 2008) and identify conditions for the classic unraveling result. In addition, I apply the theory to examples of labor markets and political campaigns. The theory explains why communication usually involves presentation of evidence and randomization over messages. So far, my work has been a preliminary step for the solution of a question with a bigger picture --- how to understand the nature of uncertainty and the essence of human's communication mode. To fulfill this objective, I will need to go back to the fundamental theory of modelling incomplete information games, and explore definitions of the unknown, knowledge, and utilities at the basic level. I believe that a better understanding of the basics is necessary for the analysis of the complex. Only by developing a novel method to analyze the fundamental question, will I be able to grasp the deeper feature of human behavior which is of interest in Information Economics.