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When will the Range of Prizes in Tournaments Increase in the Noise or in the Number of Players?

Author

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  • Yigal Gerchak

    (Department of Industrial Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel)

  • Qi-Ming He

    (Department of Industrial Engineering, Daltech, Dalhausie University, Halifax, N.S., Canada B3J 2X4, Canada)

Abstract

The symmetric equilibrium resulting from the celebrated Tournament model of Lazear and Rosen has a range of compensation between winner and loser which is inversely proportional toE[f(X)], the expectation of the additive noise's density. There seems to be a belief that this functional is always increasing in the noise's variability, which would agree with economic intuition — when output is noisier it should be less worthwhile to work hard. We show that such is not the case for some distributions, and characterize classes where such is or is not the case. When the number of playersngrows, winning is more difficult so we would expect the required range of compensation to be larger. That would require thatE[f(Y)], whereY =max(X1,…,Xn-1), will decrease inn. We examine the generality of this property. Finally we explore the same issues within a multiplicative model.

Suggested Citation

  • Yigal Gerchak & Qi-Ming He, 2003. "When will the Range of Prizes in Tournaments Increase in the Noise or in the Number of Players?," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 151-165.
    • Handle: RePEc:wsi:igtrxx:v:05:y:2003:i:02:n:s0219198903000957
    DOI: 10.1142/S0219198903000957
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    References listed on IDEAS

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    1. Hvide, Hans K. & Kristiansen, Eirik G., 2003. "Risk taking in selection contests," Games and Economic Behavior, Elsevier, vol. 42(1), pages 172-179, January.
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    Cited by:

    1. Christoph March & Marco Sahm, 2019. "The Perks of Being in the Smaller Team: Incentives in Overlapping Contests," CESifo Working Paper Series 7994, CESifo.
    2. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    3. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    4. Sheremeta, Roman & Masters, William & Cason, Timothy, 2009. "Contests with Random Noise and a Shared Prize," MPRA Paper 58271, University Library of Munich, Germany.
    5. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    6. Song, Jian & Houser, Daniel, 2023. "Asymmetric shocks in contests: Theory and experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 216(C), pages 243-267.
    7. Mikhail Drugov & Dmitry Ryvkin, 2019. "The shape of luck and competition in tournaments," Working Papers w0251, Center for Economic and Financial Research (CEFIR).
    8. Cason, Timothy N. & Masters, William A. & Sheremeta, Roman M., 2020. "Winner-take-all and proportional-prize contests: Theory and experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 175(C), pages 314-327.
    9. Ryvkin, Dmitry, 2010. "The selection efficiency of tournaments," European Journal of Operational Research, Elsevier, vol. 206(3), pages 667-675, November.
    10. John A. List & Daan van Soest & Jan Stoop & Haiwen Zhou, 2020. "On the Role of Group Size in Tournaments: Theory and Evidence from Laboratory and Field Experiments," Management Science, INFORMS, vol. 66(10), pages 4359-4377, October.
    11. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    12. Merve İntişah & Mürüvvet Büyükboyacı, 2024. "The role of noise variance on effort in group contests," Theory and Decision, Springer, vol. 97(2), pages 311-346, September.
    13. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    14. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Winner-Take-All Tournaments," CEPR Discussion Papers 12067, C.E.P.R. Discussion Papers.
    15. Laurence Ales & Soo‐Haeng Cho & Ersin Körpeoğlu, 2021. "Innovation Tournaments with Multiple Contributors," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1772-1784, June.
    16. Ryvkin, Dmitry & Drugov, Mikhail, 2020. "The shape of luck and competition in winner-take-all tournaments," Theoretical Economics, Econometric Society, vol. 15(4), November.
    17. Xu Tian & Gongbing Bi, 2022. "Multiplicative output form and its applications to problems in the homogenous innovation contest model," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(3), pages 709-732, September.

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    More about this item

    Keywords

    Tournaments; prizes; noise; number of players;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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