Title: Essays on Communication in Game Theory
Description: This dissertation consists of essays on communication in game theory. The first chapter develops a model of dynamic persuasion. A sender has a fixed number of pieces of hard evidence that contain information about the quality of his proposal, each of which is either favorable or unfavorable. The sender may try to persuade a decision maker (DM) that she has enough favorable evidence by sequentially revealing at most one piece at a time. Presenting evidence is costly for the sender and delaying decisions is costly for the DM. I study the equilibria of the resulting dynamic communication game. The sender effectively chooses when to give up persuasion and the DM decides when to make a decision. Resolving the strategic tension requires probabilistic behavior from both parties. Typically, the DM will accept the sender's proposal even when she knows that the sender's evidence may be overall unfavorable. However, in a Pareto efficient equilibrium, the other type of error does not occur unless delays costs are very large.

Furthermore, the sender's net gain from engaging in persuasion can be negative on the equilibrium path, even when persuasion is successful. we perform comparative statics in the costs of persuasion. I also characterize the DM's optimal stochastic commitment rule and the optimal non-stochastic commitment rule; compared to the communication game, the former yields a Pareto improvement, whereas, the latter can leave even the DM either better or worse off. The second chapter studies a unidimensional Hotelling-Downs model of electoral competition with the following innovation: a fraction of candidates have "competence", which is unobservable to voters. In our model, competence means the ability to correctly observe a policy-relevant state of the world. This structure induces a signaling game between competent and incompetent candidates. We show that in equilibrium, proposing an extreme platform serves as a signal about competence, and has a strictly higher winning probability than that of the median platform.

Polarization happens and the degree of it depends on how uncertain the state is and how much political candidates are office-motivated. The third chapter examines the dynamic extension of Che, Dessein, and Kartik (2011). They study strategic communication by an agent who has non-verifiable private information about different alternatives. The agent does not internalize the principal's benefit from her outside option. They show that a pandering distortion arises in communication. This chapter studies the long-run consequence of their model when a new agent-principal pair is formed in each period, and principals in later periods may learn some information from predecessors' actions. I show that informational cascade, in which communication completely breaks down, can arise, even when communication can benefit both parties. I also characterize the conditions under which effective communication between principal and agent can continue in perpetuity.