Title: Essays in Economic Theory
Description: This dissertation consists of four essays in economic theory. All of them fall under the umbrella of economics of information; we study various models of game-theoretic interaction between players who are communicating with others, and have (or are able to produce) information of some sort. There is a large emphasis on the interplay of information, incentives and beliefs. In the first chapter we study a model of communication and persuasion between a sender who is privately informed and has state independent preferences, and a receiver who has preferences that depend on the unknown state. In a model with two states of the world, over the interesting range of parameters, the equilibria can be pooling or separating, but a particular novel refinement forces the pooling to be on the most informative information structure in interesting cases. We also study two extensions - a model with more information structures as well as a model where the state of the world is non-dichotomous, and show that analogous results emerge.

In the second chapter, which is coauthored with Joseph E. Stiglitz and Jungyoll Yun, we study the Rothschild-Stiglitz model of competitive insurance markets with endogenous information disclosure by both firms and consumers. We show that an equilibrium always exists, (even without the single crossing property), and characterize the unique equilibrium allocation. With two types of consumers the outcome is particularly simple, consisting of a pooling allocation which maximizes the well-being of the low risk individual (along the zero profit pooling line) plus a supplemental (undisclosed and nonexclusive) contract that brings the high risk individual to full insurance (at his own odds). We also show that this outcome is extremely robust and Pareto efficient. In the third chapter we study a game of strategic information design between a sender, who chooses state-dependent information structures, a mediator who can then garble the signals generated from these structures, and a receiver who takes an action after observing the signal generated by the first two players.

Among the results is a novel (and complete, in a special case) characterization of the set of posterior beliefs that are achievable given a fixed garbling. We characterize a simple sufficient condition for the unique equilibrium to be uninformative, and provide comparative statics with regard to the mediator’s preferences, the number of mediators, and different informational arrangements. In the fourth chapter we study a novel equilibrium refinement - belief-payoff monotonicity. We introduce a definition, argue that it is reasonable since it captures an attractive intuition, relate the refinement to others in the literature and study some of the properties.