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Bayesian Persuasion

Paper Session

Saturday, Jan. 4, 2020 10:15 AM - 12:15 PM (PDT)

Marriott Marquis, Carlsbad
Hosted By: Econometric Society
  • Chair: Fei Li, University of North Carolina-Chapel Hill

Belief Meddling in Social Networks: An Information-Design Approach

Simone Galperti
,
University of California-San Diego
Jacopo Perego
,
Columbia University

Abstract

Abstract: Social media have become an increasingly important source of information about political, social and economic issues. While beneficial on many levels, the decentralized nature of these media may expose societies to novel risks of manipulation by third parties. To evaluate these risks, we study a model where a designer sends information to agents who interact in a game, so as to affect its outcome. The designer can communicate only with a limited number of agents, who then share information with each other on a network of social links before playing the game. We characterize the equilibrium outcomes that can be induced by seeding this social network with information. Our main result recasts this constrained information-design problem in terms of an equivalent linear program, which is particularly useful for applications. We show that a simple property of the network---the depth of communication---fully determines the scope for belief manipulation. Finally, we illustrate how a holistic use of linear-programming duality helps to characterize the solution to the optimal seeding problem. Our theory offers insights into the design of advertisement and political campaigns that are robust to (or leverage on) information spillovers.

Censorship as Optimal Persuasion

Anton Kolotilin
,
University of New South Wales
Tymofiy Mylovanov
,
University of Pittsburgh
Andriy Zapechelnyuk
,
University of St. Andrews

Abstract

A sender designs a signal about the state of the world to persuade a receiver. Under standard assumptions, an optimal signal censors states on one side of a cutoff and reveals all other states. This result holds in continuous and discrete environments with general and monotone partitional signals. The sender optimally censors more information if she is more biased, if she is more certain about the receiver’s preferences, and if the receiver is easier to persuade. We apply our results to the problem of media censorship by a government.

Bayesian Persuasion with Costly Messages

Anh Nguyen
,
Carnegie Mellon University
Teck Yong Tan
,
Nanyang Technological University

Abstract

We study a model of Bayesian persuasion in which the Sender publicly designs a signal structure, privately observes the signal realization and then reports a message to the Receiver at a cost that depends on the signal realization. We provide sufficient conditions for full information revelation by the Sender, and these conditions are satisfied under many commonly studied communication games. Under these conditions, the Sender's (lack of) commitment in the persuasion problem is quantified as a communication cost to sustain the chosen belief distribution. The value of persuasion is shown to be the Sender's utility under his most preferred equilibrium within the set of equilibria with full information revelation in the given communication game. We apply this approach to study test design and a lobbyist's incentive to generate and truthfully report new information to policy-makers.

Simultaneous Versus Sequential Disclosure

Peicong Hu
,
University of California-San Diego
Joel Sobel
,
University of California-San Diego

Abstract

We study an environment in which a decision maker has access to several expert advisers. The experts all have access to an identical set of facts. The decision maker's utility is increasing in the number of facts that the experts reveal. The experts have (potentially) different preferences. The game in which experts simultaneously disclose information typically has multiple equilibria. When multiple equilibria exist, the decision maker's favorite equilibrium fails to survive iterative deletion of weakly dominated strategies. We characterize the set of equilibria that survive iterative deletion of weakly dominated strategies. In a leading special case, only one outcome survives iterative deletion of weakly dominated strategies. It is the most preferred equilibrium from the perspective of the experts. We study the outcomes that can arise when the decision maker can consult the experts sequentially. We demonstrate that if the decision maker can select the order of consultations, can consult experts multiple times, and can commit to ending the consultation process, then in leading cases he can induce the same disclosure as with simultaneous disclosure. Sequential disclosure may perform worse than simultaneous disclosure from the perspective of the decision maker when it is not possible to consult experts multiple times or if commitment is not feasible.

Sequential Persuasion

Fei Li
,
University of North Carolina-Chapel Hill
Peter Norman
,
University of North Carolina-Chapel Hill

Abstract

This paper studies sequential Bayesian persuasion games with multiple senders. We provide a tractable characterization of equilibrium outcomes. We apply the model to study how the structure of consultations affects information revelation. Adding a sender who moves first cannot reduce informativeness in equilibrium, and results in a more informative equilibrium in the case of two states. Moreover, with the exception of the first sender, it is without loss of generality to let each sender move only once. Sequential persuasion cannot generate a more informative equilibrium than simultaneous persuasion and is always less informative when there are only two states. Finally, we provide a simple condition that guarantees that full revelation is the unique equilibrium outcome regardless of the ordering of senders.
JEL Classifications
  • D8 - Information, Knowledge, and Uncertainty
  • C7 - Game Theory and Bargaining Theory