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A Rothschild-Stiglitz Approach to Bayesian Persuasion


  • Matthew Gentzkow
  • Emir Kamenica


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

    1. repec:wly:emetrp:v:85:y:2017:i:6:p:1949-1964 is not listed on IDEAS
    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, March.
    5. 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.
    6. Yun Wang, 2015. "Bayesian Persuasion with Multiple Receivers," Working Papers 2015-03-24, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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    Cited by:

    1. repec:eee:jetheo:v:177:y:2018:i:c:p:34-69 is not listed on IDEAS
    2. Anton Kolotilin & Andriy Zapechelnyuk, 2018. "Persuasion Meets Delegation," Discussion Papers 2018-06, School of Economics, The University of New South Wales.
    3. Artem Hulko & Mark Whitmeyer, 2018. "Information Provision in a Sequential Search Setting," Papers 1802.09396,, revised Jun 2018.
    4. Leal Vizcaíno René & Mekonnen Teddy, 2019. "Bayesian Comparative Statics," Working Papers 2019-03, Banco de México.
    5. Romanyuk, Gleb & Smolin, Alexey, 2018. "Cream Skimming and Information Design in Marching Markets," MPRA Paper 86713, University Library of Munich, Germany.
    6. Anton Kolotilin & Hongyi, 2018. "Relational Communication," Discussion Papers 2018-12, School of Economics, The University of New South Wales.
    7. Artem Hulko & Mark Whitmeyer, 2017. "A Game of Random Variables," Papers 1712.08716,, revised Apr 2018.
    8. Anton Kolotilin & Hongyi Li, 2019. "Relational Communication," Papers 1901.05645,
    9. Joseph Whitmeyer & Mark Whitmeyer, 2019. "Mixtures of Mean-Preserving Contractions," Papers 1905.05157,
    10. Anton Kolotilin & Hongyi, 2019. "Relational Communication," Discussion Papers 2018-12a, School of Economics, The University of New South Wales.

    More about this item

    JEL classification:

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


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