Essays on persuasion and disclosure

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2022-08-05

Authors

Jiang, Shaofei, Ph. D.

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This dissertation consists of three chapters in microeconomic theory with a focus on persuasion games and disclosure games. I study how valuable information about an unknown state of the world is acquired by an economic agent (the sender) and communicated to another agent (the receiver) with conflicting interest. Applications considered include drug approval, startup funding, and disclosure of proprietary information.

In the first chapter, I study a model of costly Bayesian persuasion by a privately and partially informed sender who acquires information through a public experiment. I microfound the cost of an experiment via a Wald's sequential sampling problem and show that it equals the expected reduction in a weighted log-likelihood ratio function evaluated at the sender's belief. I focus on equilibria satisfying the D1 criterion. The equilibrium outcome depends on the relative costs of getting good and bad news in the experiment. If bad news is more costly, there exists a unique separating equilibrium outcome, more information is acquired because of sender private information, and the receiver unambiguously benefits from the sender's private information. If good news is sufficiently more costly, the single-crossing property fails. There exists a continuum of pooling equilibria, and the receiver strictly suffers from sender private information in some pooling equilibria.

In the second chapter, I study a disclosure game with a large evidence space. There is an unknown binary state. A sender observes a sequence of binary signals about the state and discloses a left truncation of the sequence to a receiver in order to convince him that the state is good. I focus on truth-leaning equilibria (c.f. Hart et al., 2017), where the sender discloses truthfully when doing so is optimal, and the receiver takes off-path disclosure at face value. In equilibrium, seemingly sub-optimal truncations are disclosed, and the disclosure contains the longest truncation that yields the maximal difference between the number of good and bad signals. The analysis falls under a general framework of disclosure games which can accommodate large evidence spaces, a wide range of disclosure technologies, and finitely many states. I characterize the unique equilibrium value function of the sender and propose a method to construct equilibria for a broad class of disclosure games.

In the third chapter, I study equilibrium refinement in finite action disclosure games. Hart et al. (2017) show that a truth-leaning equilibrium yields the same outcome as the optimal mechanism where the receiver commits ex ante to an action plan, and it is equivalent to an equilibrium of a perturbed game where the sender has an infinitesimal reward for disclosing truthfully. I show that, when the receiver's action space is finite, truth-leaning equilibrium may fail to exist, and it is not equivalent to equilibrium of the perturbed game. Moreover, the receiver can achieve higher payoffs with commitment power. I introduce a disturbed game with a small uncertainty about the receiver's payoff. A purifiable equilibrium is a truth-leaning equilibrium in an infinitesimally disturbed game. It exists and is receiver optimal. A truth-leaning equilibrium that is also purifiable is an equilibrium of the perturbed game.

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