Competing Persuaders in Zero-Sum Games

We study a Bayesian Persuasion game with multiple senders employing conditionally independent experiments. Senders have zero-sum preferences over what information is revealed. We characterize when a set of states cannot be pooled in any equilibrium, and in particular, when the state is (fully) revealed in every equilibrium. The state must be fully revealed in every equilibrium if and only if sender utility functions are sufficiently nonlinear. In the binary-state case, the state is fully revealed in every equilibrium if and only if some sender has nontrivial preferences. Our takeaway is that `most' zero-sum sender preferences result in full revelation.Comment: Version 1, August 202

Bayesian Persuasion

When is it possible for one person to persuade another to change her action? We take a mechanism design approach to this question. Taking preferences and initial beliefs as given, we introduce the notion of a persuasion mechanism: a game between Sender and Receiver defined by an information structure and a message technology. We derive necessary and sufficient conditions for the existence of a persuasion mechanism that strictly benefits Sender. We characterize the optimal mechanism. Finally, we analyze several examples that illustrate the applicability of our results.

Competitive Information Disclosure with Multiple Receivers

This paper analyzes a model of competition in Bayesian persuasion in which two symmetric senders vie for the patronage of multiple receivers by disclosing information about the qualities (i.e., binary state -- high or low) of their respective proposals. Each sender is allowed to commit to a signaling policy where he sends a private (possibly correlated) signal to every receiver. The sender's utility is a monotone set function of receivers who make a patron to this sender. We characterize the equilibrium structure and show that the equilibrium is not unique (even for simple utility functions). We then focus on the price of stability (PoS) in the game of two senders -- the ratio between the best of senders' welfare (i.e., the sum of two senders' utilities) in one of its equilibria and that of an optimal outcome. When senders' utility function is anonymous submodular or anonymous supermodular, we analyze the relation between PoS with the ex ante qualities $\lambda$ (i.e., the probability of high quality) and submodularity or supermodularity of utility functions. In particular, in both families of utility function, we show that $\text{PoS} = 1$ when the ex ante quality $\lambda$ is weakly smaller than $1/2$, that is, there exists equilibrium that can achieve welfare in the optimal outcome. On the other side, we also prove that $\text{PoS} > 1$ when the ex ante quality $\lambda$ is larger than $1/2$, that is, there exists no equilibrium that can achieve the welfare in the optimal outcome. We also derive the upper bound of $\text{PoS}$ as a function of $\lambda$ and the properties of the value function. Our analysis indicates that the upper bound becomes worse as the ex ante quality $\lambda$ increases or the utility function becomes more supermodular (resp.\ submodular)

Persuasion with Coarse Communication

Persuasion is an exceedingly difficult task. A leading cause of this difficulty is the misalignment of preferences, which is studied extensively by the literature on persuasion games. However, the difficulty of communication also has a first order effect on the outcomes and welfare of agents. Motivated by this observation, we study a model of Bayesian Persuasion in which the communication between the sender and the receiver is constrained. This is done by allowing the cardinality of the signal space to be less than the cardinality of the action space and the state space, which limits the number of action recommendations that the sender can make. Existence of a maximum to the sender's problem is proven and its properties are characterized. This generalizes the standard Bayesian Persuasion framework, in which existence results rely on the assumption of rich signal spaces. We analyze the sender's willingness to pay for an additional signal as a function of the prior belief, which can be interpreted as the value of precise communication. We provide an upper bound for this value which applies to all finite persuasion games. While increased precision is always better for the sender, we show that the receiver might prefer coarse communication. We show this by analyzing a game of advice seeking, where the receiver has the ability to choose the size of the signal space

Collective Sampling: An Ex Ante Perspective

I study collective dynamic information acquisition. Players determine when to end sequential sampling via a collective choice rule. My analysis focuses on the case of two players, but extends to many players. With two players, collective stopping is determined either unilaterally or unanimously. I develop a methodology to characterize equilibrium outcomes using an ex ante perspective on posterior distributions. Under unilateral stopping, each player chooses a mean-preserving contraction of the other's posterior distribution; under unanimous stopping, they choose meanpreserving spreads. Equilibrium outcomes can be determined via concavification. Players learn Pareto inefficiently: too little under unilateral stopping, while too much under unanimous stopping; these learning inefficiencies are amplified when players' preferences become less aligned. I demonstrate the value of my methodological approach in three applications: committee search, dynamic persuasion, and competition in persuasion

Essays in Economic Theory: Strategic Communication and Information Design

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