IDEAS home Printed from https://ideas.repec.org/p/grt/wpegrt/2019-07.html
   My bibliography  Save this paper

Contests with an uncertain number of prizes

Author

Listed:
  • François Maublanc
  • Sébastien Rouillon

Abstract

We study multiple-prize contests where the number of prizes to be awarded is a random variable. We determine the symmetric Nash equilibrium of the contest game. We analyze the equilibrium outcome from the perspective of a contest designer aiming at maximizing the aggregate contest expenditure. Assuming that the total value at stake is non-increasing in the number of prizes, we show that the aggregate contest expenditure decreases with the expectation on the number of prizes (first-order stochastic dominance), with the risk in the number of prizes (second-order stochastic dominance), and increases with the number of contestants. We give sufficient conditions such that the same holds under a general specification. Accordingly, a contest designer aiming at maximizing the aggregate contest expenditure should always award a single prize, reveal this information to the contestants and open the contest game to all potential participants.

Suggested Citation

  • François Maublanc & Sébastien Rouillon, 2019. "Contests with an uncertain number of prizes," Cahiers du GREThA (2007-2019) 2019-07, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    • Handle: RePEc:grt:wpegrt:2019-07
    as

    Download full text from publisher

    File URL: http://cahiersdugretha.u-bordeaux.fr/2019/2019-07.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nava Kahana & Doron Klunover, 2015. "A note on Poisson contests," Public Choice, Springer, vol. 165(1), pages 97-102, October.
    2. Jean-Michel Courtault & Bertrand Crettez & Naïla Hayek, 2006. "Characterization of Stochastic Dominance for Discrete Random Variable," Post-Print halshs-00446413, HAL.
    3. Dana Sisak, 2009. "Multiple‐Prize Contests – The Optimal Allocation Of Prizes," Journal of Economic Surveys, Wiley Blackwell, vol. 23(1), pages 82-114, February.
    4. Roger Myerson & Karl Wärneryd, 2006. "Population uncertainty in contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 469-474, January.
    5. Szymanski, Stefan & Valletti, Tommaso M., 2005. "Incentive effects of second prizes," European Journal of Political Economy, Elsevier, vol. 21(2), pages 467-481, June.
    6. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    7. Lim, Wooyoung & Matros, Alexander, 2009. "Contests with a stochastic number of players," Games and Economic Behavior, Elsevier, vol. 67(2), pages 584-597, November.
    8. Clark, Derek J & Riis, Christian, 1996. "A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-184, April.
    9. Berry, S Keith, 1993. "Rent-Seeking with Multiple Winners," Public Choice, Springer, vol. 77(2), pages 437-443, October.
    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. Maublanc, François & Rouillon, Sébastien, 2023. "Contests with an uncertain number of prizes with a fixed total value," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 20-25.
    2. 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.
    3. Yaron Azrieli & Christopher P. Chambers, 2024. "Success functions in large contests," Papers 2403.07152, arXiv.org, revised May 2024.
    4. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2023. "On equilibrium uniqueness in generalized multi-prize nested lottery contests," Games and Economic Behavior, Elsevier, vol. 139(C), pages 180-199.
    5. Lu, Jingfeng & Shen, Bo & Wang, Zhewei, 2017. "Optimal contest design under reverse-lottery technology," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 25-35.
    6. Alberto Vesperoni, 2016. "A contest success function for rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 905-937, December.
    7. Jingfeng Lu & Zhewei Wang, 2016. "Axiomatization of reverse nested lottery contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 939-957, December.
    8. Jia, Hao & Sun, Ching-jen, 2021. "The optimal entry fee-prize ratio in Tullock contests," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    9. Boris Ginzburg, 2021. "Optimal Price Of Entry Into A Competition," Economic Inquiry, Western Economic Association International, vol. 59(1), pages 280-286, January.
    10. Boosey, Luke & Brookins, Philip & Ryvkin, Dmitry, 2017. "Contests with group size uncertainty: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 105(C), pages 212-229.
    11. Kim, Bara & Yoo, Seung Han, 2021. "Population uncertainty and revealing contestants," Economics Letters, Elsevier, vol. 199(C).
    12. Fu, Qiang & Lu, Jingfeng & Wang, Zhewei, 2014. "“Reverse” nested lottery contests," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 128-140.
    13. Sela, Aner, 2016. "The Optimal Allocation of Punishments in Tullock Contests," CEPR Discussion Papers 11592, C.E.P.R. Discussion Papers.
    14. Marco Serena, 2022. "Harnessing beliefs to optimally disclose contestants’ types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 763-792, October.
    15. Lu, Jingfeng & Wang, Zhewei, 2015. "Axiomatizing multi-prize nested lottery contests: A complete and strict ranking perspective," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 127-141.
    16. Liqun Liu & Nicolas Treich, 2021. "Optimality of winner-take-all contests: the role of attitudes toward risk," Journal of Risk and Uncertainty, Springer, vol. 63(1), pages 1-25, August.
    17. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    18. Fu, Qiang & Lu, Jingfeng, 2007. "Unifying Contests: from Noisy Ranking to Ratio-Form Contest Success Functions," MPRA Paper 6679, University Library of Munich, Germany.
    19. Luke Boosey & Philip Brookins & Dmitry Ryvkin, 2020. "Information Disclosure in Contests with Endogenous Entry: An Experiment," Management Science, INFORMS, vol. 66(11), pages 5128-5150, November.
    20. XiaoGang Che & Brad Humphreys, 2014. "Contests with a Prize Externality and Stochastic Entry," Working Papers 14-19, Department of Economics, West Virginia University.

    More about this item

    Keywords

    Contest model · Rent-seeking · Multiple-prizes · Number uncertainty · Incomplete information;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    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:grt:wpegrt:2019-07. 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: Ernest Miguelez (email available below). General contact details of provider: https://edirc.repec.org/data/ifredfr.html .

    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.