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Mixtures of mean-preserving contractions

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  • Whitmeyer, Joseph
  • Whitmeyer, Mark

Abstract

Given any purely atomic probability distribution with support on n points, P, any mean-preserving contraction (mpc) of P, Q, with support on m>n points is a mixture of mpcs of P, each with support on at most n points. We illustrate several applications of this result to Bayesian persuasion and information design.

Suggested Citation

  • Whitmeyer, Joseph & Whitmeyer, Mark, 2021. "Mixtures of mean-preserving contractions," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    • Handle: RePEc:eee:mateco:v:94:y:2021:i:c:s0304406820301270
    DOI: 10.1016/j.jmateco.2020.11.006
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    References listed on IDEAS

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    1. Au, Pak Hung & Kawai, Keiichi, 2020. "Competitive information disclosure by multiple senders," Games and Economic Behavior, Elsevier, vol. 119(C), pages 56-78.
    2. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
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    6. Luis Rayo & Ilya Segal, 2010. "Optimal Information Disclosure," Journal of Political Economy, University of Chicago Press, vol. 118(5), pages 949-987.
    7. 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.
    8. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    9. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
    10. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
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