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Private Bayesian persuasion with sequential games

Private Bayesian persuasion with sequential games
Private Bayesian persuasion with sequential games
We study an information-structure design problem (a.k.a. a persuasion problem) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal probability distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the much more expressive case in which the receivers interact in a sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ by the time at which the receivers commit to following the sender’s signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the sender’s expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. Instead, in contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to the novel algorithm we propose, based on the ellipsoid method.
AAAI Press
Celli, Andrea
676d63f9-935b-48f6-82a8-578a1cb4fd95
Coniglio, Stefano
03838248-2ce4-4dbc-a6f4-e010d6fdac67
Gatti, Nicola
0c84554d-64dd-45ae-b4b2-aeeb0d30aea2
Celli, Andrea
676d63f9-935b-48f6-82a8-578a1cb4fd95
Coniglio, Stefano
03838248-2ce4-4dbc-a6f4-e010d6fdac67
Gatti, Nicola
0c84554d-64dd-45ae-b4b2-aeeb0d30aea2

Celli, Andrea, Coniglio, Stefano and Gatti, Nicola (2019) Private Bayesian persuasion with sequential games. In Proceedings of the AAAI Conference on Artificial Intelligence. AAAI Press. 9 pp . (In Press)

Record type: Conference or Workshop Item (Paper)

Abstract

We study an information-structure design problem (a.k.a. a persuasion problem) with a single sender and multiple receivers with actions of a priori unknown types, independently drawn from action-specific marginal probability distributions. As in the standard Bayesian persuasion model, the sender has access to additional information regarding the action types, which she can exploit when committing to a (noisy) signaling scheme through which she sends a private signal to each receiver. The novelty of our model is in considering the much more expressive case in which the receivers interact in a sequential game with imperfect information, with utilities depending on the game outcome and the realized action types. After formalizing the notions of ex ante and ex interim persuasiveness (which differ by the time at which the receivers commit to following the sender’s signaling scheme), we investigate the continuous optimization problem of computing a signaling scheme which maximizes the sender’s expected revenue. We show that computing an optimal ex ante persuasive signaling scheme is NP-hard when there are three or more receivers. Instead, in contrast with previous hardness results for ex interim persuasion, we show that, for games with two receivers, an optimal ex ante persuasive signaling scheme can be computed in polynomial time thanks to the novel algorithm we propose, based on the ellipsoid method.

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Accepted/In Press date: 11 November 2019

Identifiers

Local EPrints ID: 435896
URI: http://eprints.soton.ac.uk/id/eprint/435896
PURE UUID: cf09c001-95eb-42e8-8671-9de3646ed5ab
ORCID for Stefano Coniglio: ORCID iD orcid.org/0000-0001-9568-4385

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Date deposited: 22 Nov 2019 17:30
Last modified: 17 Mar 2024 03:40

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Contributors

Author: Andrea Celli
Author: Nicola Gatti

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