39 Pages Posted: 25 Jan 2016 Last revised: 25 Jul 2017
Date Written: September 30, 2016
We consider a multi-agent 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 he sends a private signal to every receiver. The payoff to the sender is a function of the subset of adopters and the realized state. We characterize an optimal signaling policy and the maximal revenue to the sender for three different types of payoff functions: supermodular, symmetric submodular, and a supermajority function. Moreover, we provide a necessary and sufficient conditions under which a public and conditionally independent signaling policy is optimal.
Keywords: Bayesian Persuasion, Information Revelation
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