Optimal Persuasion via Bi-Pooling

39 Pages Posted: 23 Jan 2020 Last revised: 5 Feb 2020

See all articles by Itai Arieli

Itai Arieli

Technion-Israel Institute of Technology

Yakov Babichenko

Technion, Industrial Engineering and Managemenet

Rann Smorodinsky

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Takuro Yamashita

University of Toulouse 1 - Toulouse School of Economics (TSE)

Date Written: December 30, 2019

Abstract

The canonical Bayesian persuasion setting studies a model where an informed agent, the Sender, can partially share his information with an uninformed agent, the Receiver. The Receiver's utility is a function of the state of nature and the Receiver's action while the Sender's is only a function of the Receiver's action. The classical results characterize the Sender's optimal information disclosure policy whenever the state space is finite. In this paper we study the same setting where the state space is an interval on the real line. We introduce the class of {\it bi-pooling policies} and the induced distribution over posteriors which we refer to as \emph{bi-pooling distributions}. We show that this class of distributions characterizes the set of optimal distributions in the aforementioned setting. Every persuasion problem admits an optimal bi-pooling distribution as a solution. Conversely, for every bi-pooling distribution there exists a persuasion problem in which the given distribution is the \emph{unique} optimal one. We leverage this result to study the structure of the price function in this setting and to identify optimal information disclosure policies.

Suggested Citation

Arieli, Itai and Babichenko, Yakov and Smorodinsky, Rann and Yamashita, Takuro, Optimal Persuasion via Bi-Pooling (December 30, 2019). Available at SSRN: https://ssrn.com/abstract=3511516 or http://dx.doi.org/10.2139/ssrn.3511516

Itai Arieli (Contact Author)

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000
Israel

Yakov Babichenko

Technion, Industrial Engineering and Managemenet ( email )

Hiafa, 3434113
Israel

Rann Smorodinsky

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel

Takuro Yamashita

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

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