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Algorithmic aspects of private Bayesian persuasion.

Babichenko, Y and Barman, S (2017) Algorithmic aspects of private Bayesian persuasion. In: 8th Innovations in Theoretical Computer Science Conference, ITCS 2017, 9 - 11 January 2017, Berkeley.

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Official URL: https://doi.org/10.4230/LIPIcs.ITCS.2017.34


We consider a multi-receivers Bayesian persuasion model where an informed sender tries to persuade a group of receivers to take a certain action. The state of nature is known to the sender, but it is unknown to the receivers. The sender is allowed to commit to a signaling policy where she sends a private signal to every receiver. This work studies the computation aspects of finding a signaling policy that maximizes the sender's revenue. We show that if the sender's utility is a submodular function of the set of receivers that take the desired action, then we can efficiently find a signaling policy whose revenue is at least (1 - 1/e) times the optimal. We also prove that approximating the sender's optimal revenue by a factor better than (1 - 1/e) is NP-hard and, hence, the developed approximation guarantee is essentially tight. When the sender's utility is a function of the number of receivers that take the desired action (i.e., the utility function is anonymous), we show that an optimal signaling policy can be computed in polynomial time. Our results are based on an interesting connection between the Bayesian persuasion problem and the evaluation of the concave closure of a set function.

Item Type: Conference Paper
Publication: Leibniz International Proceedings in Informatics, LIPIcs
Publisher: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Additional Information: The copyright for this article belongs to the Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing.
Keywords: Economics; Polynomial approximation; Signal receivers; Signaling, Algorithmic aspects; Bayesian; Concave Closure; Economics of information; Optimal signaling; Polynomial-time; Submodular functions; Utility functions, Optimization
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 17 Jul 2022 05:34
Last Modified: 17 Jul 2022 05:34
URI: https://eprints.iisc.ac.in/id/eprint/74460

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