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A Rothschild-Stiglitz Approach to Bayesian Persuasion

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  • Matthew Gentzkow
  • Emir Kamenica

Abstract

Rothschild and Stiglitz (1970) represent random variables as convex functions (integrals of the cumulative distribution function). Combining this representation with Blackwell's Theorem (1953), we characterize distributions of posterior means that can be induced by a signal. This characterization provides a novel way to analyze a class of Bayesian persuasion problems.

Suggested Citation

  • Matthew Gentzkow & Emir Kamenica, 2016. "A Rothschild-Stiglitz Approach to Bayesian Persuasion," American Economic Review, American Economic Association, vol. 106(5), pages 597-601, May.
  • Handle: RePEc:aea:aecrev:v:106:y:2016:i:5:p:597-601
    Note: DOI: 10.1257/aer.p20161049
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    References listed on IDEAS

    as
    1. Anton Kolotilin & Tymofiy Mylovanov & Andriy Zapechelnyuk & Ming Li, 2017. "Persuasion of a Privately Informed Receiver," Econometrica, Econometric Society, vol. 85(6), pages 1949-1964, November.
    2. Anton Kolotilin, 2013. "Optimal Information Disclosure: Quantity vs. Quality," Discussion Papers 2013-19, School of Economics, The University of New South Wales.
    3. Rothschild, Michael & Stiglitz, Joseph E., 1972. "Addendum to "increasing risk: I. A definition"," Journal of Economic Theory, Elsevier, vol. 5(2), pages 306-306, October.
    4. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, February.
    5. Yun Wang, 2015. "Bayesian Persuasion with Multiple Receivers," Working Papers 2015-03-24, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Anton Kolotilin & Alexander Wolitzky, 2020. "Assortative Information Disclosure," Discussion Papers 2020-08, School of Economics, The University of New South Wales.
    2. Anton Kolotilin & Hongyi, 2018. "Relational Communication," Discussion Papers 2018-12, School of Economics, The University of New South Wales.
    3. Goldstein, Itay & Leitner, Yaron, 2018. "Stress tests and information disclosure," Journal of Economic Theory, Elsevier, vol. 177(C), pages 34-69.
    4. Armstrong, Mark & Zhou, Jidong, 2019. "Consumer information and the limits to competition," CEPR Discussion Papers 14162, C.E.P.R. Discussion Papers.
    5. Dizdar, Deniz & Kováč, Eugen, 2020. "A simple proof of strong duality in the linear persuasion problem," Games and Economic Behavior, Elsevier, vol. 122(C), pages 407-412.
    6. Anton Kolotilin & Andriy Zapechelnyuk, 2018. "Persuasion Meets Delegation," Discussion Papers 2018-06, School of Economics, The University of New South Wales.
    7. Pak Hung Au & Mark Whitmeyer, 2018. "Attraction Versus Persuasion," Papers 1802.09396, arXiv.org, revised Feb 2021.
    8. René Leal Vizcaíno & Teddy Mekonnen, 2019. "Bayesian Comparative Statics," Working Papers 2019-03, Banco de México.
    9. Maxim Ivanov, 0. "Optimal monotone signals in Bayesian persuasion mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 0, pages 1-46.
    10. Ozan Candogan & Philipp Strack, 2021. "Optimal Disclosure of Information to a Privately Informed Receiver," Papers 2101.10431, arXiv.org, revised Mar 2021.
    11. Romanyuk, Gleb & Smolin, Alexey, 2018. "Cream Skimming and Information Design in Marching Markets," MPRA Paper 86713, University Library of Munich, Germany.
    12. Elliot Lipnowski & Doron Ravid, 2020. "Cheap Talk With Transparent Motives," Econometrica, Econometric Society, vol. 88(4), pages 1631-1660, July.
    13. Francis de Véricourt, & Huseyin Gurkan, & Shouqiang Wang,, 2020. "Informing the public about a pandemic," ESMT Research Working Papers ESMT-20-03, ESMT European School of Management and Technology, revised 11 Feb 2021.
    14. Maryam Saeedi & Ali Shourideh, 2020. "Optimal Rating Design," Papers 2008.09529, arXiv.org, revised Sep 2020.
    15. Anton Kolotilin & Tymofiy Mylovanov & Andriy Zapechelnyuk, 2019. "Censorship as Optimal Persuasion," Discussion Paper Series, School of Economics and Finance 201903, School of Economics and Finance, University of St Andrews, revised 05 Mar 2020.
    16. Zhou, Jidong, 2019. "Mixed Bundling in Oligopoly Markets," MPRA Paper 97432, University Library of Munich, Germany.
    17. Azarmsa, Ehsan & Cong, Lin William, 2020. "Persuasion in relationship finance," Journal of Financial Economics, Elsevier, vol. 138(3), pages 818-837.
    18. Artem Hulko & Mark Whitmeyer, 2017. "A Game of Random Variables," Papers 1712.08716, arXiv.org, revised Apr 2018.
    19. S. Nageeb Ali & Nima Haghpanah & Xiao Lin & Ron Siegel, 2020. "How to Sell Hard Information," Papers 2010.08037, arXiv.org.
    20. Doval, Laura & Skreta, Vasiliki, 2021. "Purchase history and product personalization," CEPR Discussion Papers 15969, C.E.P.R. Discussion Papers.
    21. Feng, Xin, 2020. "Information disclosure on the contest mechanism," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 148-156.
    22. Ginzburg, Boris, 2019. "Optimal information censorship," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 377-385.
    23. Joseph Whitmeyer & Mark Whitmeyer, 2019. "Mixtures of Mean-Preserving Contractions," Papers 1905.05157, arXiv.org, revised Sep 2020.
    24. Piotr Dworczak & Anton Kolotilin, 2019. "The Persuasion Duality," Papers 1910.11392, arXiv.org.

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    More about this item

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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