IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1712.08716.html
   My bibliography  Save this paper

A Game of Random Variables

Author

Listed:
  • Artem Hulko
  • Mark Whitmeyer

Abstract

This paper analyzes a simple game with $n$ players. We fix a mean, $\mu$, in the interval $[0, 1]$ and let each player choose any random variable distributed on that interval with the given mean. The winner of the zero-sum game is the player whose random variable has the highest realization. We show that the position of the mean within the interval is paramount. Remarkably, if the given mean is above a crucial threshold then the unique equilibrium must contain a point mass on $1$. The cutoff is strictly decreasing in the number of players, $n$; and for fixed $\mu$, as the number of players is increased, each player places more weight on $1$ at equilibrium. We characterize the equilibrium as the number of players goes to infinity.

Suggested Citation

  • Artem Hulko & Mark Whitmeyer, 2017. "A Game of Random Variables," Papers 1712.08716, arXiv.org, revised Apr 2018.
  • Handle: RePEc:arx:papers:1712.08716
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1712.08716
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anne-Katrin Roesler & Balázs Szentes, 2017. "Buyer-Optimal Learning and Monopoly Pricing," American Economic Review, American Economic Association, vol. 107(7), pages 2072-2080, July.
    2. 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.
    3. Skreta, Vasiliki & Perez-Richet, Eduardo, 2017. "Information Design under Falsification," CEPR Discussion Papers 12271, C.E.P.R. Discussion Papers.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pak Hung Au & Mark Whitmeyer, 2018. "Attraction versus Persuasion: Information Provision in Search Markets," Papers 1802.09396, arXiv.org, revised May 2022.
    2. Eduardo Perez‐Richet & Vasiliki Skreta, 2022. "Test Design Under Falsification," Econometrica, Econometric Society, vol. 90(3), pages 1109-1142, May.
    3. Maryam Saeedi & Ali Shourideh, 2020. "Optimal Rating Design under Moral Hazard," Papers 2008.09529, arXiv.org, revised Jul 2023.
    4. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    5. Kocourek, Pavel & Steiner, Jakub & Stewart, Colin, 2024. "Boundedly rational demand," Theoretical Economics, Econometric Society, vol. 19(4), November.
    6. Thomas Mariotti & Nikolaus Schweizer & Nora Szech & Jonas von Wangenheim, 2023. "Information Nudges and Self-Control," Management Science, INFORMS, vol. 69(4), pages 2182-2197, April.
    7. Zhou, Jidong, 2021. "Mixed bundling in oligopoly markets," Journal of Economic Theory, Elsevier, vol. 194(C).
    8. Ginzburg, Boris, 2019. "Optimal information censorship," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 377-385.
    9. repec:spo:wpecon:info:hdl:2441/31aa5v8jtp9p48jlhrq44psjoa is not listed on IDEAS
    10. Gottardi, Piero & Mezzetti, Claudio, 2024. "Shuttle diplomacy," Journal of Economic Theory, Elsevier, vol. 216(C).
    11. Tsakas, Elias & Tsakas, Nikolas, 2021. "Noisy persuasion," Games and Economic Behavior, Elsevier, vol. 130(C), pages 44-61.
    12. Kai Hao Yang & Alexander K. Zentefis, 2023. "Extreme Points of First-Order Stochastic Dominance Intervals: Theory and Applications," Cowles Foundation Discussion Papers 2355, Cowles Foundation for Research in Economics, Yale University.
    13. Maxim Ivanov, 2021. "Optimal monotone signals in Bayesian persuasion mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 955-1000, October.
    14. Anton Kolotilin & Andriy Zapechelnyuk, 2018. "Persuasion Meets Delegation," Discussion Papers 2018-06, School of Economics, The University of New South Wales.
    15. Zeng, Yishu, 2023. "Derandomization of persuasion mechanisms," Journal of Economic Theory, Elsevier, vol. 212(C).
    16. Ichihashi, Shota & Smolin, Alex, 2023. "Buyer-Optimal Algorithmic Consumption," CEPR Discussion Papers 18476, C.E.P.R. Discussion Papers.
    17. Kolotilin, Anton & Li, Hongyi, 2021. "Relational communication," Theoretical Economics, Econometric Society, vol. 16(4), November.
    18. Kai Hao Yang & Alexander K. Zentefis, 2022. "Gerrymandering and the Limits of Representative Democracy," Cowles Foundation Discussion Papers 2328, Cowles Foundation for Research in Economics, Yale University.
    19. Ludmila Matyskova, 2018. "Bayesian Persuasion with Costly Information Acquisition," CERGE-EI Working Papers wp614, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    20. Arieli, Itai & Babichenko, Yakov & Smorodinsky, Rann & Yamashita, Takuro, 2023. "Optimal persuasion via bi-pooling," Theoretical Economics, Econometric Society, vol. 18(1), January.
    21. Mark Armstrong & Jidong Zhou, 2022. "Consumer Information and the Limits to Competition," American Economic Review, American Economic Association, vol. 112(2), pages 534-577, February.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1712.08716. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.