IDEAS home Printed from https://ideas.repec.org/p/awi/wpaper/0600.html
   My bibliography  Save this paper

A theory of knockout tournament seedings

Author

Listed:
  • Karpov, Alexander

Abstract

This paper provides nested sets and vector representations of knockout tournaments. The paper introduces classification of probability domain assumptions and a new set of axioms. Two new seeding methods are proposed: equal gap seeding and increasing competitive intensity seeding. Under different probability domain assumptions, several axiomatic justifications are obtained for equal gap seeding. A discrete optimization approach is developed. It is applied to justify equal gap seeding and increasing competitive intensity seeding. Some justification for standard seeding is obtained. Combinatorial properties of the seedings are studied.

Suggested Citation

  • Karpov, Alexander, 2015. "A theory of knockout tournament seedings," Working Papers 0600, University of Heidelberg, Department of Economics.
    • Handle: RePEc:awi:wpaper:0600
    Note: This paper is part of http://archiv.ub.uni-heidelberg.de/volltextserver/view/schriftenreihen/sr-3.html
    as

    Download full text from publisher

    File URL: http://nbn-resolving.de/urn/resolver.pl?urn=urn:nbn:de:bsz:16-heidok-192311
    File Function: Frontdoor page on HeiDOK
    Download Restriction: no
    File URL: https://archiv.ub.uni-heidelberg.de/volltextserver/19231/1/karpov_2015_dp600.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Matthias Kräkel, 2014. "Optimal seedings in elimination tournaments revisited," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 77-91, April.
    2. Baumann Robert & Matheson Victor A. & Howe Cara A., 2010. "Anomalies in Tournament Design: The Madness of March Madness," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(2), pages 1-11, April.
    3. Baker, Rose D. & McHale, Ian G., 2014. "A dynamic paired comparisons model: Who is the greatest tennis player?," European Journal of Operational Research, Elsevier, vol. 236(2), pages 677-684.
    4. Dmitry Ryvkin, 2009. "Tournaments of Weakly Heterogeneous Players," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(5), pages 819-855, October.
    5. Jacobson, Sheldon H. & Nikolaev, Alexander G. & King, Douglas M. & Lee, Adrian J., 2011. "Seed distributions for the NCAA men's basketball tournament," Omega, Elsevier, vol. 39(6), pages 719-724, December.
    6. Roger G. Noll, 2003. "The Organization of Sports Leagues," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 19(4), pages 530-551, Winter.
    7. 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.
    8. Khatibi, Arash & King, Douglas M. & Jacobson, Sheldon H., 2015. "Modeling the winning seed distribution of the NCAA Division I men׳s basketball tournament," Omega, Elsevier, vol. 50(C), pages 141-148.
    9. Rudi Stracke & Wolfgang Höchtl & Rudolf Kerschbamer & Uwe Sunde, 2015. "Incentives and Selection in Promotion Contests: Is It Possible to Kill Two Birds with One Stone?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 36(5), pages 275-285, July.
    10. Gent Bajraj & Levent Ülkü, 2015. "Choosing two finalists and the winner," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 729-744, December.
    11. Jeff Horen & Raymond Riezman, 1985. "Comparing Draws for Single Elimination Tournaments," Operations Research, INFORMS, vol. 33(2), pages 249-262, April.
    12. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    13. Sonin, Konstantin & Dagaev, Dmitry, 2013. "Winning by Losing: Incentive Incompatibility in Multiple Qualifiers," CEPR Discussion Papers 9373, C.E.P.R. Discussion Papers.
    14. Beck A. Taylor & Justin G. Trogdon, 2002. "Losing to Win: Tournament Incentives in the National Basketball Association," Journal of Labor Economics, University of Chicago Press, vol. 20(1), pages 23-41, January.
    15. Dmitry Dagaev & Alex Suzdaltsev, 2015. "Seeding, Competitive Intensity and Quality in Knock-Out Tournaments," HSE Working papers WP BRP 91/EC/2015, National Research University Higher School of Economics.
    16. Kfir Eliaz & Michael Richter & Ariel Rubinstein, 2011. "Choosing the two finalists," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 211-219, February.
    17. Boulier, Bryan L. & Stekler, H. O., 1999. "Are sports seedings good predictors?: an evaluation," International Journal of Forecasting, Elsevier, vol. 15(1), pages 83-91, February.
    18. Stern, Hal, 1992. "Are all linear paired comparison models empirically equivalent?," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 103-117, February.
    19. Wright, Mike, 2014. "OR analysis of sporting rules – A survey," European Journal of Operational Research, Elsevier, vol. 232(1), pages 1-8.
    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. Amelia Bădică & Costin Bădică & Ion Buligiu & Liviu Ion Ciora & Doina Logofătu, 2021. "Dynamic Programming Algorithms for Computing Optimal Knockout Tournaments," Mathematics, MDPI, vol. 9(19), pages 1-24, October.

    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. Sela, Aner, 2022. "Effort allocations in elimination tournaments," Economics Letters, Elsevier, vol. 211(C).
    2. Arlegi, Ritxar & Dimitrov, Dinko, 2020. "Fair elimination-type competitions," European Journal of Operational Research, Elsevier, vol. 287(2), pages 528-535.
    3. Dmitry Dagaev & Alex Suzdaltsev, 2018. "Competitive intensity and quality maximizing seedings in knock-out tournaments," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 170-188, January.
    4. Netanel Nissim & Aner Sela, 2020. "The Third Place Game," Journal of Sports Economics, , vol. 21(1), pages 64-86, January.
    5. Hörtnagl-Pozzo, Tanja & Kerschbamer, Rudolf & Oexl, Regine & Stracke, Rudi & Sunde, Uwe, 2023. "Heterogeneity in rent-seeking contests with multiple stages: Theory and experimental evidence," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 105(C).
    6. Chen Cohen & Ishay Rabi & Aner Sela, 2023. "Optimal seedings in interdependent contests," Annals of Operations Research, Springer, vol. 328(2), pages 1263-1285, September.
    7. Ritxar Arlegi & Institute for Advanced Research in Business and Economics (INARBE) & Dinko Dimitrov, 2018. "Fair Competition Design," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1803, Departamento de Economía - Universidad Pública de Navarra.
    8. Ira Horowitz, 2018. "Competitive Balance in the NBA Playoffs," The American Economist, Sage Publications, vol. 63(2), pages 215-227, October.
    9. Csató, László, 2023. "How to avoid uncompetitive games? The importance of tie-breaking rules," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1260-1269.
    10. Dmitry Dagaev & Konstantin Sonin, 2018. "Winning by Losing," Journal of Sports Economics, , vol. 19(8), pages 1122-1146, December.
    11. Jun Zhang, 2008. "Simultaneous Signaling In Elimination Contests," Working Paper 1184, Economics Department, Queen's University.
    12. Deck, Cary & Kimbrough, Erik O., 2015. "Single- and double-elimination all-pay tournaments," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 416-429.
    13. Jennifer Brown & Dylan B. Minor, 2014. "Selecting the Best? Spillover and Shadows in Elimination Tournaments," Management Science, INFORMS, vol. 60(12), pages 3087-3102, December.
    14. Vong, Allen I.K., 2017. "Strategic manipulation in tournament games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 562-567.
    15. Lackner, Mario & Stracke, Rudi & Sunde, Uwe & Winter-Ebmer, Rudolf, 2020. "Are competitors forward looking in strategic interactions? Field evidence from multistage tournaments," Journal of Economic Behavior & Organization, Elsevier, vol. 179(C), pages 544-565.
    16. Karlsson, Niklas & Lunander, Anders, 2020. "Choosing Opponents in Skiing Sprint Elimination Tournaments," Working Papers 2020:6, Örebro University, School of Business, revised 01 Sep 2020.
    17. Kovenock, Dan & Konrad, Kai A., 2006. "Multi-Stage Contests with Stochastic Ability," CEPR Discussion Papers 5844, C.E.P.R. Discussion Papers.
    18. Dmitry Dagaev & Alex Suzdaltsev, 2015. "Seeding, Competitive Intensity and Quality in Knock-Out Tournaments," HSE Working papers WP BRP 91/EC/2015, National Research University Higher School of Economics.
    19. 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.
    20. Segev, Ella & Sela, Aner, 2014. "Multi-stage sequential all-pay auctions," European Economic Review, Elsevier, vol. 70(C), pages 371-382.

    More about this item

    Keywords

    elimination tournament; competitive intensity; fairness; economics of sport.;
    All these keywords.

    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:awi:wpaper:0600. 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: Gabi Rauscher (email available below). General contact details of provider: https://edirc.repec.org/data/awheide.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.