IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2601.22112.html

Distributional Competition

Author

Listed:
  • Mark Whitmeyer

Abstract

I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must possess, and provide a characterization via the first-order approach. Manifold applications--to R&D competition, oligopolistic competition with product design, and rank-order contests--follow.

Suggested Citation

  • Mark Whitmeyer, 2026. "Distributional Competition," Papers 2601.22112, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2601.22112
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2601.22112
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Scott M Gilpatric, 2009. "Risk Taking In Contests And The Role Of Carrots And Sticks," Economic Inquiry, Western Economic Association International, vol. 47(2), pages 266-277, April.
    2. Sudipto Bhattacharya & Dilip Mookherjee, 1986. "Portfolio Choice in Research and Development," RAND Journal of Economics, The RAND Corporation, vol. 17(4), pages 594-605, Winter.
    3. Liad Wagman & Vincent Conitzer, 2012. "Choosing fair lotteries to defeat the competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 91-129, February.
    4. Au, Pak Hung & Kawai, Keiichi, 2020. "Competitive information disclosure by multiple senders," Games and Economic Behavior, Elsevier, vol. 119(C), pages 56-78.
    5. Henrique Castro-Pires & Deniz Kattwinkel & Jan Knoepfle, 2025. "Who and How? Adverse Selection and flexible Moral Hazard," Papers 2506.12979, arXiv.org, revised Sep 2025.
    6. Raphael Boleslavsky & Christopher Cotton, 2015. "Grading Standards and Education Quality," American Economic Journal: Microeconomics, American Economic Association, vol. 7(2), pages 248-279, May.
    7. Han Feng & David Hobson, 2015. "Gambling in contests modelled with diffusions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 21-37, April.
    8. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    9. Mark Whitmeyer, 2019. "Relative performance concerns among investment managers," Annals of Finance, Springer, vol. 15(2), pages 205-231, June.
    10. Hvide, Hans K. & Kristiansen, Eirik G., 2003. "Risk taking in selection contests," Games and Economic Behavior, Elsevier, vol. 42(1), pages 172-179, January.
    11. Kim, Kyungmin & Koh, Youngwoo, 2022. "Auctions with flexible information acquisition," Games and Economic Behavior, Elsevier, vol. 133(C), pages 256-281.
    12. Aryel. Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 165-184, Springer.
    13. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    14. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
    15. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    16. Whitmeyer, Mark, 2023. "Submission costs in risk-taking contests," Games and Economic Behavior, Elsevier, vol. 142(C), pages 101-112.
    17. Doron Ravid & Anne-Katrin Roesler & Balázs Szentes, 2022. "Learning before Trading: On the Inefficiency of Ignoring Free Information," Journal of Political Economy, University of Chicago Press, vol. 130(2), pages 346-387.
    18. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    19. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
    20. ,, 2006. "Competition over agents with boundedly rational expectations," Theoretical Economics, Econometric Society, vol. 1(2), pages 207-231, June.
    21. Tor Klette & David de Meza, 1986. "Is the Market Biased Against Risky R&D?," RAND Journal of Economics, The RAND Corporation, vol. 17(1), pages 133-139, Spring.
    22. Hans K. Hvide, 2002. "Tournament Rewards and Risk Taking," Journal of Labor Economics, University of Chicago Press, vol. 20(4), pages 877-898, October.
    23. Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-857, July.
    24. Raphael Boleslavsky & Christopher Cotton, 2018. "Limited capacity in project selection: competition through evidence production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 385-421, March.
    25. Jeffrey M. Perloff & Steven C. Salop, 1985. "Equilibrium with Product Differentiation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(1), pages 107-120.
    26. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
    27. Pak Hung Au & Mark Whitmeyer, 2023. "Attraction versus Persuasion: Information Provision in Search Markets," Journal of Political Economy, University of Chicago Press, vol. 131(1), pages 202-245.
    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. Whitmeyer, Mark, 2023. "Submission costs in risk-taking contests," Games and Economic Behavior, Elsevier, vol. 142(C), pages 101-112.
    2. Mark Whitmeyer, 2021. "Submission Fees in Risk-Taking Contests," Papers 2108.13506, arXiv.org.
    3. Cohen, Chen & Lagziel, David & Levi, Ofer & Sela, Aner, 2023. "The role of the second prize in all-pay auctions with two heterogeneous prizes," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    4. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2019. "A general framework for studying contests," MPRA Paper 97363, University Library of Munich, Germany.
    5. HHironori Otsubo, 2012. "Contests with Incumbency Advantages: An Experiment Investigation of the Effect of Limits on Spending Behavior and Outcome," Jena Economics Research Papers 2012-020, Friedrich-Schiller-University Jena.
    6. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    7. Cohen, Chen & Sela, Aner, 2008. "Allocation of prizes in asymmetric all-pay auctions," European Journal of Political Economy, Elsevier, vol. 24(1), pages 123-132, March.
    8. Minchuk, Yizhaq & Sela, Aner, 2014. "All-pay auctions with certain and uncertain prizes," Games and Economic Behavior, Elsevier, vol. 88(C), pages 130-134.
    9. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Chen Cohen & David Lagziel & Ofer Levi & Aner Sela, 2020. "All-Pay Auctions With Heterogeneous Prizes And Partially Asymmetric Players," Working Papers 2010, Ben-Gurion University of the Negev, Department of Economics.
    11. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.
    12. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    13. Myatt, David P., 2025. "The impact of perceived strength in the war of attrition," Games and Economic Behavior, Elsevier, vol. 150(C), pages 260-277.
    14. Florian Morath & Johannes Münster, 2013. "Information acquisition in conflicts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 99-129, September.
    15. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    16. Ella Segev & Aner Sela, 2014. "Sequential all-pay auctions with head starts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 893-923, December.
    17. Segev, Ella & Sela, Aner, 2014. "Sequential all-pay auctions with noisy outputs," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 251-261.
    18. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    19. Au, Pak Hung & Kawai, Keiichi, 2020. "Competitive information disclosure by multiple senders," Games and Economic Behavior, Elsevier, vol. 119(C), pages 56-78.
    20. He, Wei & Li, Jiangtao, 2023. "Competitive information disclosure in random search markets," Games and Economic Behavior, Elsevier, vol. 140(C), pages 132-153.

    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:2601.22112. 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.