IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v05y2003i02ns0219198903000957.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198903000957
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198903000957?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. Hvide, Hans K. & Kristiansen, Eirik G., 2003. "Risk taking in selection contests," Games and Economic Behavior, Elsevier, vol. 42(1), pages 172-179, January.
    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. Christoph March & Marco Sahm, 2019. "The Perks of Being in the Smaller Team: Incentives in Overlapping Contests," CESifo Working Paper Series 7994, CESifo.
    2. Mikhail Drugov & Dmitry Ryvkin, 2019. "The shape of luck and competition in tournaments," Working Papers w0251, New Economic School (NES).
    3. 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.
    4. 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.
    5. Ryvkin, Dmitry & Drugov, Mikhail, 2020. "The shape of luck and competition in winner-take-all tournaments," Theoretical Economics, Econometric Society, vol. 15(4), November.
    6. 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.
    7. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    8. Ryvkin, Dmitry, 2010. "The selection efficiency of tournaments," European Journal of Operational Research, Elsevier, vol. 206(3), pages 667-675, November.
    9. Sheremeta, Roman & Masters, William & Cason, Timothy, 2009. "Contests with Random Noise and a Shared Prize," MPRA Paper 58271, University Library of Munich, Germany.
    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. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    12. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    13. Morgan, John & Tumlinson, Justin & Várdy, Felix, 2022. "The limits of meritocracy," Journal of Economic Theory, Elsevier, vol. 201(C).
    14. 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.
    15. Song, Jian & Houser, Daniel, 2023. "Asymmetric shocks in contests: Theory and experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 216(C), pages 243-267.
    16. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Winner-Take-All Tournaments," CEPR Discussion Papers 12067, C.E.P.R. Discussion Papers.

    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. Anja Schöttner & Veikko Thiele, 2010. "Promotion Tournaments and Individual Performance Pay," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(3), pages 699-731, September.
    2. Sudipto Bhattacharya & Pojanart Sunirand, 2012. "Banks, Relative Performance, and Sequential Contagion," Chapters, in: The Challenge of Financial Stability, chapter 7, pages 153-170, Edward Elgar Publishing.
    3. Eriksen, Kristoffer W. & Kvaløy, Ola, 2014. "Myopic risk-taking in tournaments," Journal of Economic Behavior & Organization, Elsevier, vol. 97(C), pages 37-46.
    4. Li, Bo & Wu, Zenan & Xing, Zeyu, 2023. "Optimally biased contests with draws," Economics Letters, Elsevier, vol. 226(C).
    5. Ewerhart, Christian, 2016. "An envelope approach to tournament design," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 1-9.
    6. J. Atsu Amegashie, 2009. "American Idol: should it be a singing contest or a popularity contest?," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 33(4), pages 265-277, November.
    7. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Biased contests for symmetric players," Games and Economic Behavior, Elsevier, vol. 103(C), pages 116-144.
    8. José A. García Martínez, 2005. "Selection And Efficiency In Hierarchical Social Systems," Working Papers. Serie AD 2005-35, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Tor Eriksson & Sabrina Teyssier & Marie‐Claire Villeval, 2009. "Self‐Selection And The Efficiency Of Tournaments," Economic Inquiry, Western Economic Association International, vol. 47(3), pages 530-548, July.
    10. Konrad, Kai A., 2014. "Search duplication in research and design spaces — Exploring the role of local competition," International Journal of Industrial Organization, Elsevier, vol. 37(C), pages 222-228.
    11. Münster, Johannes, 2006. "Selection Tournaments, Sabotage, and Participation," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 118, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    12. Sajid Ullah & Farman Ullah Khan & Laura-Mariana Cismaș & Muhammad Usman & Andra Miculescu, 2022. "Do Tournament Incentives Matter for CEOs to Be Environmentally Responsible? Evidence from Chinese Listed Companies," IJERPH, MDPI, vol. 19(1), pages 1-20, January.
    13. Oliver Gürtler, 2006. "Are 18 Holes Enough for Tiger Woods?," Bulletin of Economic Research, Wiley Blackwell, vol. 58(3), pages 267-284, July.
    14. Suzuki, Toru, 2012. "Competitive problem solving and the optimal prize schemes," Games and Economic Behavior, Elsevier, vol. 75(2), pages 1009-1013.
    15. González-Díaz, Julio & Palacios-Huerta, Ignacio, 2016. "Cognitive performance in competitive environments: Evidence from a natural experiment," Journal of Public Economics, Elsevier, vol. 139(C), pages 40-52.
    16. Mark Whitmeyer, 2021. "Submission Fees in Risk-Taking Contests," Papers 2108.13506, arXiv.org.
    17. Mueller-Langer Frank & Andreoli-Versbach Patrick, 2017. "Leading-Effect, Risk-Taking and Sabotage in Two-Stage Tournaments: Evidence from a Natural Experiment," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 237(1), pages 1-28, February.
    18. Kräkel, Matthias, 2008. "Optimal risk taking in an uneven tournament game with risk averse players," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1219-1231, December.
    19. March, Christoph & Sahm, Marco, 2018. "Contests as selection mechanisms: The impact of risk aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 114-131.
    20. Jose Apesteguia & Ignacio Palacios-Huerta, 2010. "Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment," American Economic Review, American Economic Association, vol. 100(5), pages 2548-2564, December.

    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

    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:wsi:igtrxx:v:05:y:2003:i:02:n:s0219198903000957. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.