IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v96y2021ics0304406821000781.html
   My bibliography  Save this article

The optimal entry fee-prize ratio in Tullock contests

Author

Listed:
  • Jia, Hao
  • Sun, Ching-jen

Abstract

We analyze a three-stage game where an organizer sets an entry fee for a Tullock contest event, and a finite population of homogeneous agents simultaneously decide whether to participate or not. We show that in the unique symmetric subgame perfect Nash equilibrium, the larger the population size, the lower the probability the agents enter the contest, but the organizer’s optimal entry fee-prize ratio could either increase or decrease with the population size. When the population size approaches infinity, the number of contestants converges to a Poisson distributed random variable.

Suggested Citation

  • Jia, Hao & Sun, Ching-jen, 2021. "The optimal entry fee-prize ratio in Tullock contests," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    • Handle: RePEc:eee:mateco:v:96:y:2021:i:c:s0304406821000781
    DOI: 10.1016/j.jmateco.2021.102515
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406821000781
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2021.102515?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Christian Ewerhart, 2015. "Mixed equilibria in Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 59-71, September.
    2. Amegashie, J Atsu, 1999. "The Design of Rent-Seeking Competitions: Committees, Preliminary and Final Contests," Public Choice, Springer, vol. 99(1-2), pages 63-76, April.
    3. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-294, March.
    4. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    5. Richard Higgins & William Shughart & Robert Tollison, 1985. "Efficient rents 2 free entry and efficient rent seeking," Public Choice, Springer, vol. 46(3), pages 247-258, January.
    6. Gene M. Grossman & Elhanan Helpman, 1996. "Electoral Competition and Special Interest Politics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(2), pages 265-286.
    7. Ewerhart, Christian, 2017. "Revenue ranking of optimally biased contests: The case of two players," Economics Letters, Elsevier, vol. 157(C), pages 167-170.
    8. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    9. William Corcoran, 1984. "Long-run equilibrium and total expenditures in rent-seeking," Public Choice, Springer, vol. 43(1), pages 89-94, January.
    10. Qiang Fu & Qian Jiao & Jingfeng Lu, 2015. "Contests with endogenous entry," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 387-424, May.
    11. Nava Kahana & Doron Klunover, 2015. "A note on Poisson contests," Public Choice, Springer, vol. 165(1), pages 97-102, October.
    12. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603, Decembrie.
    13. 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.
    14. Thomas, Jonathan P. & Wang, Zhewei, 2013. "Optimal punishment in contests with endogenous entry," Journal of Economic Behavior & Organization, Elsevier, vol. 91(C), pages 34-50.
    15. Lim, Wooyoung & Matros, Alexander, 2009. "Contests with a stochastic number of players," Games and Economic Behavior, Elsevier, vol. 67(2), pages 584-597, November.
    16. Robert Michaels, 1988. "The design of rent-seeking competitions," Public Choice, Springer, vol. 56(1), pages 17-29, January.
    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. Jiao, Qian & Ke, Changxia & Liu, Yang, 2022. "When to disclose the number of contestants: Theory and experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 193(C), pages 146-160.
    2. Nava Kahana & Doron Klunover, 2015. "A note on Poisson contests," Public Choice, Springer, vol. 165(1), pages 97-102, October.
    3. Jingfeng Lu & Hongkun Ma & Zhe Wang, 2018. "Ranking Disclosure Policies In All‐Pay Auctions," Economic Inquiry, Western Economic Association International, vol. 56(3), pages 1464-1485, July.
    4. Kahana, Nava & Klunover, Doron, 2016. "Complete rent dissipation when the number of rent seekers is uncertain," Economics Letters, Elsevier, vol. 141(C), pages 8-10.
    5. Arye L. Hillman & Ngo Van Long, 2017. "Rent Seeking: The Social Cost of Contestable Benefits," CESifo Working Paper Series 6462, CESifo.
    6. 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.
    7. XiaoGang Che & Brad Humphreys, 2014. "Contests with a Prize Externality and Stochastic Entry," Working Papers 14-19, Department of Economics, West Virginia University.
    8. Arye Hillman & Ngo Van Long, 2017. "The social cost of contestable benefits," CIRANO Working Papers 2017s-11, CIRANO.
    9. 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.
    10. Kim, Bara & Yoo, Seung Han, 2021. "Population uncertainty and revealing contestants," Economics Letters, Elsevier, vol. 199(C).
    11. Gu, Yiquan & Hehenkamp, Burkhard & Leininger, Wolfgang, 2019. "Evolutionary equilibrium in contests with stochastic participation: Entry, effort and overdissipation," Journal of Economic Behavior & Organization, Elsevier, vol. 164(C), pages 469-485.
    12. Alexander Matros, 2007. "Contests with a Stochastic Number of Players," Working Paper 323, Department of Economics, University of Pittsburgh, revised Sep 2008.
    13. 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.
    14. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    15. Gil S. Epstein & Yosef Mealem & Shmuel Nitzan, 2013. "Lotteries vs. All-Pay Auctions in Fair and Biased Contests," Economics and Politics, Wiley Blackwell, vol. 25(1), pages 48-60, March.
    16. Balart, Pau & Casas, Agustin & Troumpounis, Orestis, 2022. "Technological change, campaign spending and polarization," Journal of Public Economics, Elsevier, vol. 211(C).
    17. Aycinena, Diego & Rentschler, Lucas, 2019. "Entry in contests with incomplete information: Theory and experiments," European Journal of Political Economy, Elsevier, vol. 60(C).
    18. 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).
    19. Boris Ginzburg, 2021. "Optimal Price Of Entry Into A Competition," Economic Inquiry, Western Economic Association International, vol. 59(1), pages 280-286, January.
    20. 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.

    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:eee:mateco:v:96:y:2021:i:c:s0304406821000781. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.