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Contests where there is variation in the marginal productivity of effort

Author

Listed:
  • Nirvikar Singh

    (Economics Department, University of California, Santa Cruz, CA 95064, USA)

  • Donald Wittman

    (Economics Department, University of California, Santa Cruz, CA 95064, USA)

Abstract

We provide a characterization of participants' behavior in a contest or tournament where the marginal productivity of effort varies across contestants and individual productivity is private information. We then consider the optimal design of such a contest. We first analyze contestant behavior for the usual type of contest, where the highest output wins. Abilities need not be independently distributed. We demonstrate that there is a unique symmetric equilibrium output function, that output is increasing in ability, and that marginal effort is increasing in ability, while effort decreases when the cost of effort increases. Next we consider the case where the highest output need not win, with independently distributed abilities. We analyze the contest designer's decisions in choosing contest rules optimal from her perspective. We show that the output produced, probability of winning, and contest designer's expected revenue are generally increasing in contestants' ability. We examine the relationship between the marginal cost of producing output and marginal utility per dollar of the net award for winning.

Suggested Citation

  • Nirvikar Singh & Donald Wittman, 2001. "Contests where there is variation in the marginal productivity of effort," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 711-744.
    • Handle: RePEc:spr:joecth:v:18:y:2001:i:3:p:711-744
    Note: Received: July 30, 1998; revised version: August 7, 2000
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    Citations

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    Cited by:

    1. Curry Philip A. & Mongrain Steeve, 2009. "Deterrence in Rank-Order Tournaments," Review of Law & Economics, De Gruyter, vol. 5(1), pages 723-740, December.
    2. Dmitry Ryvkin, 2007. "Tullock contests of weakly heterogeneous players," Public Choice, Springer, vol. 132(1), pages 49-64, July.
    3. repec:elg:eechap:15325_5 is not listed on IDEAS
    4. David Perez Castrillo & David Wettstein, 2014. "Discrimination in a new model of contests with two-sided asymmetric information," Working Papers 1407, Ben-Gurion University of the Negev, Department of Economics.
    5. Harminder Battu & Clive R. Belfield & Peter J. Sloane, 2003. "Human Capital Spillovers within the Workplace: Evidence for Great Britain," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(5), pages 575-594, December.
    6. David Pérez-Castrillo & David Wettstein, 2012. "Innovation Contests," Working Papers 654, Barcelona School of Economics.
    7. Marco Runkel, 2003. "Optimal Contest Design when the Designer’s Payoff Depends on Competitive Balance," CESifo Working Paper Series 1009, CESifo.
    8. Kai Konrad, 2012. "Information alliances in contests with budget limits," Public Choice, Springer, vol. 151(3), pages 679-693, June.
    9. David Pérez‐Castrillo & David Wettstein, 2016. "Discrimination In A Model Of Contests With Incomplete Information About Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 881-914, August.
    10. Gil Epstein & Igal Milchtaich & Shmuel Nitzan & Mordechai Schwarz, 2007. "Ambiguous political power and contest efforts," Public Choice, Springer, vol. 132(1), pages 113-123, July.
    11. Matthew D. Mitchell, 2019. "Uncontestable favoritism," Public Choice, Springer, vol. 181(1), pages 167-190, October.
    12. Giuseppe Dari-Mattiacci & Eric Langlais & Bruno Lovat & Francesco Parisi, 2013. "Asymmetries in Rent-Seeking," Working Papers hal-04141218, HAL.
    13. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Schwartz, 2013. "Effort maximization in asymmetric contest games with heterogeneous contestants," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(2), pages 589-630, March.
    14. Daniel Lee, 2008. "Going once, going twice, sold! The committee assignment process as an all-pay auction," Public Choice, Springer, vol. 135(3), pages 237-255, June.
    15. 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.
    16. Junichiro Ishida, 2006. "Seniority bias in a tournament," Review of Economic Design, Springer;Society for Economic Design, vol. 10(2), pages 143-164, August.
    17. Munetomo Ando, 2004. "Overconfidence in Economic Contests," Econometric Society 2004 Far Eastern Meetings 708, Econometric Society.

    More about this item

    Keywords

    Optimal contest; Contest design; Asymmetric information; Correlated abilities.;
    All these keywords.

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • J3 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs

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