IDEAS home Printed from https://ideas.repec.org/a/eee/indorg/v50y2017icp57-90.html
   My bibliography  Save this article

Optimal prize-rationing strategy in all-pay contests with incomplete information

Author

Listed:
  • Liu, Xuyuan
  • Lu, Jingfeng

Abstract

A contest organizer (e.g., a government regulatory agency) is endowed with the capacity to provide unlimited homogeneous prizes (e.g., medals) that he can use to incentivize contestants to exert productive effort in an all-pay auction with incomplete information. Each agent, at most, wins one prize. We study the optimal number of prizes the organizer should grant in order to induce maximal expected total effort or expected highest effort from agents. Both are single peaked under mild regularity conditions. When players’ abilities follow a family of beta distributions, expected highest effort maximization requires a smaller set of prizes to be awarded; for both goals, the optimal number of prizes weakly increases when the pool of contestants expands or contestant quality improves.

Suggested Citation

  • Liu, Xuyuan & Lu, Jingfeng, 2017. "Optimal prize-rationing strategy in all-pay contests with incomplete information," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 57-90.
    • Handle: RePEc:eee:indorg:v:50:y:2017:i:c:p:57-90
    DOI: 10.1016/j.ijindorg.2016.10.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167718716303356
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijindorg.2016.10.004?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. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    2. Emmanuel Dechenaux & Dan Kovenock, 2011. "Endogenous rationing, price dispersion and collusion in capacity constrained supergames," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 29-74, May.
    3. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    4. Allen, Franklin & Faulhaber, Gerald R, 1991. "Rational Rationing," Economica, London School of Economics and Political Science, vol. 58(230), pages 189-198, May.
    5. Faravelli, Marco & Stanca, Luca, 2012. "When less is more: Rationing and rent dissipation in stochastic contests," Games and Economic Behavior, Elsevier, vol. 74(1), pages 170-183.
    6. Richard J. Gilbert & Paul Klemperer, 2000. "An Equilibrium Theory of Rationing," RAND Journal of Economics, The RAND Corporation, vol. 31(1), pages 1-21, Spring.
    7. Leonid Polishchuk & Alexander Tonis, 2013. "Endogenous contest success functions: a mechanism design approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 271-297, January.
    8. 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.
    9. Stiglitz, Joseph E & Weiss, Andrew, 1981. "Credit Rationing in Markets with Imperfect Information," American Economic Review, American Economic Association, vol. 71(3), pages 393-410, June.
    10. Glazer, Amihai & Hassin, Refael, 1988. "Optimal Contests," Economic Inquiry, Western Economic Association International, vol. 26(1), pages 133-143, January.
    11. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    12. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    13. Liu, Xuyuan & Lu, Jingfeng, 2014. "The effort-maximizing contest with heterogeneous prizes," Economics Letters, Elsevier, vol. 125(3), pages 422-425.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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).
    3. Vladimir Petkov, 2023. "Prize formation and sharing in multi-stage contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 259-289, January.
    4. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    5. Sumit Goel, 2022. "Optimal grading contests," Papers 2205.05207, arXiv.org, revised Sep 2023.
    6. Dahm, Matthias, 2018. "Semi-targeted all-pay auctions: A partial exclusion principle," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 256-282.
    7. Leppälä, Samuli, 2021. "A partially exclusive rent-seeking contest," Journal of Economic Behavior & Organization, Elsevier, vol. 187(C), pages 60-75.
    8. Wasser, Cédric & Zhang, Mengxi, 2023. "Differential treatment and the winner's effort in contests with incomplete information," Games and Economic Behavior, Elsevier, vol. 138(C), pages 90-111.

    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. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    2. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Szymanski, Stefan & Valletti, Tommaso M., 2005. "Incentive effects of second prizes," European Journal of Political Economy, Elsevier, vol. 21(2), pages 467-481, June.
    4. MacKenzie, Ian A. & Hanley, Nick & Kornienko, Tatiana, 2009. "Using contests to allocate pollution rights," Energy Policy, Elsevier, vol. 37(7), pages 2798-2806, July.
    5. Yizhaq Minchuk & Aner Sela, 2020. "Contests with insurance," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 1-22, June.
    6. Minchuk, Yizhaq & Sela, Aner, 2014. "All-pay auctions with certain and uncertain prizes," Games and Economic Behavior, Elsevier, vol. 88(C), pages 130-134.
    7. Benny Moldovanu & Aner Sela & Xianwen Shi, 2012. "Carrots And Sticks: Prizes And Punishments In Contests," Economic Inquiry, Western Economic Association International, vol. 50(2), pages 453-462, April.
    8. Krumer, Alex & Megidish, Reut & Sela, Aner, 2023. "Strategic manipulations in round-robin tournaments," Mathematical Social Sciences, Elsevier, vol. 122(C), pages 50-57.
    9. E. Feess & Gerd Muehlheusser & M. Walzl, 2008. "Unfair contests," Journal of Economics, Springer, vol. 93(3), pages 267-291, April.
      • Feess, E. & Muehlheusser, G. & Walzl, M., 2004. "Unfair contests," Research Memorandum 048, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    10. Sheremeta, Roman, 2009. "Essays on Experimental Investigation of Lottery Contests," MPRA Paper 49888, University Library of Munich, Germany.
    11. Alex Krumer & Reut Megidish & Aner Sela, 2020. "The optimal design of round-robin tournaments with three players," Journal of Scheduling, Springer, vol. 23(3), pages 379-396, June.
    12. Aner Sela, 2012. "Sequential two-prize contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 383-395, October.
    13. Aner Sela, 2018. "Reverse Contests," Working Papers 1804, Ben-Gurion University of the Negev, Department of Economics.
    14. Liu, Bin & Lu, Jingfeng & Wang, Ruqu & Zhang, Jun, 2018. "Optimal prize allocation in contests: The role of negative prizes," Journal of Economic Theory, Elsevier, vol. 175(C), pages 291-317.
    15. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    16. Fu, Qiang & Lu, Jingfeng, 2009. "The beauty of "bigness": On optimal design of multi-winner contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 146-161, May.
    17. Ando, Munetomo, 2004. "Division of a contest with identical prizes," Journal of the Japanese and International Economies, Elsevier, vol. 18(2), pages 282-297, June.
    18. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    19. 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).
    20. Chawla, Shuchi & Hartline, Jason D. & Sivan, Balasubramanian, 2019. "Optimal crowdsourcing contests," Games and Economic Behavior, Elsevier, vol. 113(C), pages 80-96.

    More about this item

    Keywords

    Multi-prize contest; Prize rationing; All-pay auction; Incomplete information;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    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:eee:indorg:v:50:y:2017:i:c:p:57-90. 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/inca/505551 .

    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.