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Contest design and optimal endogenous entry

Author

Listed:
  • Fu, Qiang
  • Lu, Jingfeng
Abstract
This paper derives the effort-maximizing contest rule and the optimal endogenous entry in a context where potential participants bear fixed entry costs. The organizer is allowed to design the contest under a fixed budget with two strategic instruments: he sets the value of the prize purse, and arranges a monetary transfer (entry subsidy or fee) for each participating contestant. In other words, the budget can either be used to subsidize participation or an entry fee can be charged to fund the prize purse. The results show that the optimally designed contest attracts exactly two participating contestants in its unique subgame perfect equilibrium (when there is a positive fixed entry cost) and extracts all the surplus from participating contestants. The study also shows that the direction and amount of the monetary transfer depend on the magnitude of the entry cost: the contest organizer subsidizes entry when contestants bear substantial entry costs, but charges an entry fee to fund the prize purse whenever the entry cost is sufficiently low.

Suggested Citation

  • Fu, Qiang & Lu, Jingfeng, 2006. "Contest design and optimal endogenous entry," MPRA Paper 945, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:945
    as

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    References listed on IDEAS

    as
    1. 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.
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    4. Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-890, September.
    5. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    6. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-545, October.
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    9. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
    10. Baye, Michael R. & Hoppe, Heidrun C., 2003. "The strategic equivalence of rent-seeking, innovation, and patent-race games," Games and Economic Behavior, Elsevier, vol. 44(2), pages 217-226, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Boris Ginzburg, 2021. "Optimal Price Of Entry Into A Competition," Economic Inquiry, Western Economic Association International, vol. 59(1), pages 280-286, January.
    2. 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.
    3. Jean-François Mercier, 2018. "Selecting contestants for a rent-seeking contest," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 927-947, September.
    4. Robert Ridlon, 2016. "Does Manufacturer Advertising Crowd‐in or Crowd‐out Retailer Advertising? An Application of an Endogenous Prize Contest with Asymmetric Players," Southern Economic Journal, John Wiley & Sons, vol. 83(2), pages 364-379, October.
    5. Gu, Yiquan & Hehenkamp, Burkhard & Leininger, Wolfgang, 2017. "The Dark Side of the Force: Evolutionary Equilibrium in Contests with Stochastic Entry," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168168, Verein für Socialpolitik / German Economic Association.
    6. Martin Grossmann, 2021. "Asymmetric Opportunities After an Unsuccessful Sports Career," Journal of Sports Economics, , vol. 22(5), pages 587-612, June.
    7. Grossmann, Martin & Dietl, Helmut, 2015. "Heterogeneous outside options in contests," European Journal of Political Economy, Elsevier, vol. 37(C), pages 280-287.
    8. 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.
    9. Franke, Jörg & Kanzow, Christian & Leininger, Wolfgang & Schwartz, Alexandra, 2014. "Lottery versus all-pay auction contests: A revenue dominance theorem," Games and Economic Behavior, Elsevier, vol. 83(C), pages 116-126.
    10. 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.
    11. Fu, Qiang & Lu, Jingfeng & Lu, Yuanzhu, 2012. "Incentivizing R&D: Prize or subsidies?," International Journal of Industrial Organization, Elsevier, vol. 30(1), pages 67-79.
    12. Giebe, Thomas, 2014. "Innovation contests with entry auction," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 165-176.
    13. 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.
    14. 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.
    15. Aycinena, Diego & Rentschler, Lucas, 2019. "Entry in contests with incomplete information: Theory and experiments," European Journal of Political Economy, Elsevier, vol. 60(C).
    16. Liqun Liu & Jack Meyer & Andrew J. Rettenmaier & Thomas R. Saving, 2018. "Risk and risk aversion effects in contests with contingent payments," Journal of Risk and Uncertainty, Springer, vol. 56(3), pages 289-305, June.
    17. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Winner-Take-All Tournaments," CEPR Discussion Papers 12067, C.E.P.R. Discussion Papers.
    18. Dongryul Lee & Joon Song, 2019. "Optimal Team Contests to Induce More Efforts," Journal of Sports Economics, , vol. 20(3), pages 448-476, April.
    19. Martin Grossmann, 2021. "Entry regulations and optimal prize allocation in parallel contests," Review of Economic Design, Springer;Society for Economic Design, vol. 25(4), pages 289-316, December.
    20. Dmitry Ryvkin & Mikhail Drugov, 2017. "Tournaments," Working Papers wp2017_03_02, Department of Economics, Florida State University.

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    More about this item

    Keywords

    Contest; Endogenous Entry; Entry Cost; Subsidy; Entry Fee;
    All these keywords.

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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