Private Bayesian Persuasion

Itai Arieli

Technion-Israel Institute of Technology

Yakov Babichenko

Technion, Industrial Engineering and Managemenet

February 17, 2016

Abstract:

We consider a multi-agent Bayesian persuasion problem where an informed sender tries to persuade a group of agents to adopt a certain product. The sender is allowed to commit to a signalling policy where she sends a private signal to every agent. The payoff to the sender is a function of the subset of adopters. We characterize an optimal signalling policy and the maximal revenue to the sender for three different types of payoff functions: supermodular, symmetric submodular, and a supermajority function. Moreover, using tools from cooperative game theory we provide a necessary and sufficient condition under which public signalling policy is optimal.

Private Bayesian Persuasion

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