IDEAS home Printed from https://ideas.repec.org/p/hig/wpaper/263-ec-2023.html
   My bibliography  Save this paper

The Optimal Design Of Elimination Tournaments With A Superstar

Author

Listed:
  • Daria Tabashnikova

    (National Research University Higher School of Economics)

  • Marina Sandomirskaia

    (National Research University Higher School of Economics)

Abstract

We study single- and double-elimination tournaments with heterogeneous players of two types: regular players and a superstar. Players choose efforts in each match with linear costs, winning with a probability calculated with the Tullock success function. We consider several designer maximization problems: total efforts, probability of winning the strongest player, and a weighted composed function. We show that a double-elimination tournament is less profitable in most cases, except when the tournament organizer is concerned about the probability that the superstar wins the tournament.

Suggested Citation

  • Daria Tabashnikova & Marina Sandomirskaia, 2023. "The Optimal Design Of Elimination Tournaments With A Superstar," HSE Working papers WP BRP 263/EC/2023, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:263/ec/2023
    as

    Download full text from publisher

    File URL: https://wp.hse.ru/data/2023/11/28/2107748879/263EC2023_merged.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    2. 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.
    3. Leif Brandes & Egon Franck & Stephan Nüesch, 2008. "Local Heroes and Superstars," Journal of Sports Economics, , vol. 9(3), pages 266-286, June.
    4. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
    5. David J. Berri & Martin B. Schmidt & Stacey L. Brook, 2004. "Stars at the Gate," Journal of Sports Economics, , vol. 5(1), pages 33-50, February.
    6. Christian Groh & Benny Moldovanu & Aner Sela & Uwe Sunde, 2012. "Optimal seedings in elimination tournaments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 59-80, January.
    7. Stefan Szymanski, 2010. "The Economic Design of Sporting Contests," Palgrave Macmillan Books, in: The Comparative Economics of Sport, chapter 1, pages 1-78, Palgrave Macmillan.
    8. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    9. David J. Berri & Martin B. Schmidt, 2006. "On the Road With the National Basketball Association's Superstar Externality," Journal of Sports Economics, , vol. 7(4), pages 347-358, November.
    10. 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.
    11. Rosen, Sherwin, 1981. "The Economics of Superstars," American Economic Review, American Economic Association, vol. 71(5), pages 845-858, December.
    12. Huang, Lingbo, 2016. "Prize and incentives in double-elimination tournaments," Economics Letters, Elsevier, vol. 147(C), pages 116-120.
    13. Charles J. Mullin & Lucia F. Dunn, 2002. "Using Baseball Card Prices to Measure Star Quality and Monopsony," Economic Inquiry, Western Economic Association International, vol. 40(4), pages 620-632, October.
    14. Hausman, Jerry A & Leonard, Gregory K, 1997. "Superstars in the National Basketball Association: Economic Value and Policy," Journal of Labor Economics, University of Chicago Press, vol. 15(4), pages 586-624, October.
    Full references (including those not matched with items on IDEAS)

    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. R. Todd Jewell, 2017. "The Effect of Marquee Players on Sports Demand," Journal of Sports Economics, , vol. 18(3), pages 239-252, April.
    2. Leif Brandes & Egon Franck & Stephan Nüesch, 2008. "Local Heroes and Superstars," Journal of Sports Economics, , vol. 9(3), pages 266-286, June.
    3. Wen-Jhan Jane, 2016. "The Effect of Star Quality on Attendance Demand," Journal of Sports Economics, , vol. 17(4), pages 396-417, May.
    4. 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.
    5. Alex Krumer & Reut Megidish & Aner Sela, 2017. "Round‐Robin Tournaments with a Dominant Player," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(4), pages 1167-1200, October.
    6. Scott D. Grimshaw & Jeffrey S. Larson, 2021. "Effect of Star Power on NBA All-Star Game TV Audience," Journal of Sports Economics, , vol. 22(2), pages 139-163, February.
    7. Sela, Aner, 2016. "The Optimal Allocation of Punishments in Tullock Contests," CEPR Discussion Papers 11592, C.E.P.R. Discussion Papers.
    8. Mario Lackner, 2016. "Teams as Superstars: Effort and Risk Taking in Rank-Order Tournaments for Women and Men," Economics working papers 2016-13, Department of Economics, Johannes Kepler University Linz, Austria.
    9. Dmitry Ryvkin & Andreas Ortmann, 2008. "The Predictive Power of Three Prominent Tournament Formats," Management Science, INFORMS, vol. 54(3), pages 492-504, March.
    10. Daniel Högele & Sascha L. Schmidt & Benno Torgler, 2012. "The Influence of Superstars on Organizational Identification of External Stakeholders: Empirical Findings from Professional Soccer," CREMA Working Paper Series 2012-18, Center for Research in Economics, Management and the Arts (CREMA).
    11. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    12. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "Tournament rewards and heavy tails," Journal of Economic Theory, Elsevier, vol. 190(C).
    13. Rittwik Chatterjee, 2013. "A Brief Survey of the Theory of Auction," South Asian Journal of Macroeconomics and Public Finance, , vol. 2(2), pages 169-191, December.
    14. Brad R. Humphreys & Candon Johnson, 2020. "The Effect of Superstars on Game Attendance: Evidence From the NBA," Journal of Sports Economics, , vol. 21(2), pages 152-175, February.
    15. Bernd Frick, 2003. "Contest Theory and Sport," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 19(4), pages 512-529, Winter.
    16. Scott M. Kaplan, 2022. "Putting a price on popularity: Evidence from superstars in the National Basketball Association," Economic Inquiry, Western Economic Association International, vol. 60(3), pages 1357-1381, July.
    17. Budzinski, Oliver & Feddersen, Arne & Kunz-Kaltenhäuser, Philipp, 2022. "Demand for TV broadcasts of UEFA Champions League games in Danish television - The impact of uncertainty of outcome, stardom, and local heroes," Ilmenau Economics Discussion Papers 165, Ilmenau University of Technology, Institute of Economics.
    18. Cedric Duvinage & Peter-J. Jost, 2019. "The Role of Referees in Professional Sports Contests," Journal of Sports Economics, , vol. 20(8), pages 1014-1050, December.
    19. Segev, Ella & Sela, Aner, 2014. "Sequential all-pay auctions with noisy outputs," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 251-261.
    20. Pradeep Dubey & Siddhartha Sahi, 2016. "Optimal Prizes," Department of Economics Working Papers 16-03, Stony Brook University, Department of Economics.

    More about this item

    Keywords

    single-elimination tournament; double-elimination tournament; tournament design; heterogeneous players; superstar;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • Z20 - Other Special Topics - - Sports Economics - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hig:wpaper:263/ec/2023. 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: Shamil Abdulaev or Shamil Abdulaev (email available below). General contact details of provider: https://edirc.repec.org/data/hsecoru.html .

    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.