TY - GEN

T1 - Algorithmic aspects of private Bayesian persuasion

AU - Babichenko, Yakov

AU - Barman, Siddharth

N1 - Funding Information:
∗ The first author was supported by Israel Science Foundation, grant # 2021296. The second author was supported in part by Ramanujan Fellowship (SB/S2/RJN-128/2015).

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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.

AB - 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.

KW - Bayesian Persuasion

KW - Concave Closure

KW - Economics of Information

KW - Signaling

UR - http://www.scopus.com/inward/record.url?scp=85025842839&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ITCS.2017.34

DO - 10.4230/LIPIcs.ITCS.2017.34

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AN - SCOPUS:85025842839

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 8th Innovations in Theoretical Computer Science Conference, ITCS 2017

A2 - Papadimitriou, Christos H.

T2 - 8th Innovations in Theoretical Computer Science Conference, ITCS 2017

Y2 - 9 January 2017 through 11 January 2017

ER -