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Private Bayesian persuasion

Author

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  • Arieli, Itai
  • Babichenko, Yakov

Abstract

We consider a multi-receiver 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 she sends a private signal to every receiver. The utility of the sender is a function of the subset of adopters and the realized state. We first consider a setting with a binary state space and no payoff externalities among receivers. We characterize an optimal signaling policy and the maximal revenue to the sender for two different types of utility functions: supermodular, and anonymous submodular. In particular, for supermodular utilities we show that the optimal policy correlates positive recommendation to adopt the product as much as possible. We generalize these results to the case of a nonbinary state space. The result for supermodular utilities is generalized to the case where receivers have payoff externalities. We also provide a necessary and sufficient condition under which public and conditionally independent signaling policies are optimal.

Suggested Citation

  • Arieli, Itai & Babichenko, Yakov, 2019. "Private Bayesian persuasion," Journal of Economic Theory, Elsevier, vol. 182(C), pages 185-217.
  • Handle: RePEc:eee:jetheo:v:182:y:2019:i:c:p:185-217
    DOI: 10.1016/j.jet.2019.04.008
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    References listed on IDEAS

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    1. Bharat Anand & Ron Shachar, 2009. "Targeted advertising as a signal," Quantitative Marketing and Economics (QME), Springer, vol. 7(3), pages 237-266, September.
    2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, September.
    3. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    4. Dirk Bergemann & Stephen Morris, 2016. "Information Design, Bayesian Persuasion, and Bayes Correlated Equilibrium," American Economic Review, American Economic Association, vol. 106(5), pages 586-591, May.
    5. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
    6. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    7. Bardhi, Arjada & Guo, Yingni, 2018. "Modes of persuasion toward unanimous consent," Theoretical Economics, Econometric Society, vol. 13(3), September.
    8. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    9. Peres, Renana & Muller, Eitan & Mahajan, Vijay, 2010. "Innovation diffusion and new product growth models: A critical review and research directions," International Journal of Research in Marketing, Elsevier, vol. 27(2), pages 91-106.
    10. Schnakenberg, Keith E., 2015. "Expert advice to a voting body," Journal of Economic Theory, Elsevier, vol. 160(C), pages 102-113.
    11. Nelson, Philip, 1974. "Advertising as Information," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 729-754, July/Aug..
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    Cited by:

    1. Ronen Gradwohl & Niklas Hahn & Martin Hoefer & Rann Smorodinsky, 2020. "Reaping the Informational Surplus in Bayesian Persuasion," Papers 2006.02048, arXiv.org.
    2. Kerman, Toygar & Herings, P. Jean-Jacques & Karos, Dominik, 2020. "Persuading Strategic Voters," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).

    More about this item

    Keywords

    Bayesian persuasion; Supermodular utility; Submodular utility;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • M37 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Advertising

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