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Contest design and optimal endogenous entry

Author

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  • 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
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    File URL: https://mpra.ub.uni-muenchen.de/945/1/MPRA_paper_945.pdf
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    References listed on IDEAS

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    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. Frank R. Lichtenberg, 1988. "Government Subsidies to Private Military R&D Investment: DOD's IR&D Policy," NBER Working Papers 2745, National Bureau of Economic Research, Inc.
    3. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-545, October.
    4. 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, pages 289-294.
    5. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    6. Yeon-Koo Che & Ian Gale, 2003. "Optimal Design of Research Contests," American Economic Review, American Economic Association, vol. 93(3), pages 646-671, June.
    7. 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.
    8. 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.
    9. Barry J. Nalebuff & Joseph E. Stiglitz, 1983. "Prices and Incentives: Towards a General Theory of Compensation and Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(1), pages 21-43, Spring.
    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.
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    Citations

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    Cited by:

    1. Giebe, Thomas, 2014. "Innovation contests with entry auction," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 165-176.
    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. Gu, Yiquan & Hehenkamp, Burkhard & Leininger, Wolfgang, 2017. "The Dark Side of the Force: Evolutionary Equilibrium in Contests with Stochastic Entry," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168168, Verein für Socialpolitik / German Economic Association.
    4. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Winner-Take-All Tournaments," CEPR Discussion Papers 12067, C.E.P.R. Discussion Papers.
    5. Grossmann, Martin & Dietl, Helmut, 2015. "Heterogeneous outside options in contests," European Journal of Political Economy, Elsevier, vol. 37(C), pages 280-287.
    6. 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.
    7. 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.
    8. 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.
    9. Dmitry Ryvkin & Mikhail Drugov, 2017. "Tournaments," Working Papers wp2017_03_02, Department of Economics, Florida State University.

    More about this item

    Keywords

    Contest; Endogenous Entry; Entry Cost; Subsidy; Entry Fee;

    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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