Private Bayesian Persuasion

52 Pages Posted: 25 Jan 2016 Last revised: 13 Mar 2019

See all articles by Itai Arieli

Itai Arieli

Technion-Israel Institute of Technology

Yakov Babichenko

Technion, Industrial Engineering and Managemenet

Date Written: March 10, 2019


We consider a multi-receiver Bayesian persuasion problem where an informed sender tries to persuade a group of receivers to adopt a certain product. The sender is allowed to commit to a signaling policy where she sends a private signal to every receiver. The utility of the sender is a function of the subset of adopters and the realized state. We first consider a setting with a binary state space and no payoff externalities among receivers. We characterize an optimal signaling policy and the maximal revenue to the sender for two different types of utility functions: supermodular, and anonymous submodular. In particular, for supermodular utilities we show that the optimal policy correlates positive recommendation to adopt the product as much as possible. We generalize these results to the case of a nonbinary state space. The result for supermodular utilities is generalized to the case where receivers have payoff externalities. We also provide a necessary and sufficient condition under which public and conditionally independent signaling policies are optimal.

Keywords: Bayesian Persuasion, Information Revelation

Suggested Citation

Arieli, Itai and Babichenko, Yakov, Private Bayesian Persuasion (March 10, 2019). Available at SSRN: or

Itai Arieli (Contact Author)

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000

Yakov Babichenko

Technion, Industrial Engineering and Managemenet ( email )

Hiafa, 3434113

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