**Working Papers**

A Role for Cheap Talk in Disclosure

This paper studies a one-sender-one-receiver disclosure game with general preferences and message structures. Drawing on techniques from

This paper studies a one-sender-one-receiver disclosure game with general preferences and message structures. Drawing on techniques from

*information design*, I provide a characterization of the Perfect Bayesian Equilibrium outcomes. I find that in every equilibrium the sender uses evidence to partition the state space, and within each partition member the sender sends messages in a way as if he was playing cheap talk. 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.Sequential Bayesian Persuasion

This paper studies a Bayesian Persuasion model in which multiple senders sequentially persuade one Receiver. Players can always observe signaling rules of prior players and their realizations. We develop a recursive concavification method to characterize the set of SPEa. We prove the existence of a special type of equilibrium, called the Silent Equilibrium, where at most one sender designs a nontrivial signaling rule. Also, we show that in zero-sum games, the truth-telling information structure is always supported in equilibrium. Finally, we make comparisons with the simultaneous multi-sender Bayesian persuasion model of Gentzkow and Kamenica (2017) and examine the impact of the order of persuasion. A geometric version of Blackwell's order is adopted for examination of informativeness.

This paper studies a Bayesian Persuasion model in which multiple senders sequentially persuade one Receiver. Players can always observe signaling rules of prior players and their realizations. We develop a recursive concavification method to characterize the set of SPEa. We prove the existence of a special type of equilibrium, called the Silent Equilibrium, where at most one sender designs a nontrivial signaling rule. Also, we show that in zero-sum games, the truth-telling information structure is always supported in equilibrium. Finally, we make comparisons with the simultaneous multi-sender Bayesian persuasion model of Gentzkow and Kamenica (2017) and examine the impact of the order of persuasion. A geometric version of Blackwell's order is adopted for examination of informativeness.

Competition in Persuasion: An Experiment (with

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 information 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.

*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 information 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.

Reciprocity with Uncertainty about Others (with

Invisibility of psychological motivation generates fundamental uncertainty about others' psychological sensitivity. But the literature of social preferences has not paid much attention to psychological uncertainty. We incorporate uncertainty about others' reciprocal motivation into existing models of reciprocity (Dufwenberg and Kirchsteiger, 2004; Rabin, 1993) and propose an equilibrium concept, called Bayesian reciprocity equilibrium. We provide an existence theorem for the equilibrium. Then, we apply the theory to solve the prisoners' dilemma. In this example, we show that a small amount of uncertainty in reciprocal motivation can eliminate cooperation via iterated elimination of dominated strategies.

*Jin Sohn*)Invisibility of psychological motivation generates fundamental uncertainty about others' psychological sensitivity. But the literature of social preferences has not paid much attention to psychological uncertainty. We incorporate uncertainty about others' reciprocal motivation into existing models of reciprocity (Dufwenberg and Kirchsteiger, 2004; Rabin, 1993) and propose an equilibrium concept, called Bayesian reciprocity equilibrium. We provide an existence theorem for the equilibrium. Then, we apply the theory to solve the prisoners' dilemma. In this example, we show that a small amount of uncertainty in reciprocal motivation can eliminate cooperation via iterated elimination of dominated strategies.

**Work in Progress**

Natural Gas Transmission Project and Air Pollution in China (with

China has built its nationwide natural gas pipelines in the past 20 years. This project is called the Natural Gas Transmission Project (NGTP). The pipeline network connects to almost all provinces of China, providing the clean energy for industry and households. This study examines the effect of NGTP on air pollution in China. We collect the U.S. satellite data to be a measurement of air pollution and use the predicted connection time of pipelines as IV. We find that connection to the pipelines reduces the air pollution by 8% at the city level.

*Kaiyin Hu*)China has built its nationwide natural gas pipelines in the past 20 years. This project is called the Natural Gas Transmission Project (NGTP). The pipeline network connects to almost all provinces of China, providing the clean energy for industry and households. This study examines the effect of NGTP on air pollution in China. We collect the U.S. satellite data to be a measurement of air pollution and use the predicted connection time of pipelines as IV. We find that connection to the pipelines reduces the air pollution by 8% at the city level.