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Random Knockout Tournaments

Author

Listed:
  • Ilan Adler

    (Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720)

  • Yang Cao

    (Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90033)

  • Richard Karp

    (Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, California 94720)

  • Erol A. Peköz

    (Questrom School of Business, Boston University, Boston, Massachusetts 02215)

  • Sheldon M. Ross

    (Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, California 90033)

Abstract

We consider a random knockout tournament among players 1,…, n , in which each match involves two players. The match format is specified by the number of matches played in each round, where the constitution of the matches in a round is random. Supposing that there are numbers v 1 ,…, v n such that a match between i and j will be won by i with probability v i /( v i + v j ), we obtain a lower bound on the tournament win probability for the best player, as well as upper and lower bounds for all of the players. We also obtain additional bounds by considering the best and worst formats for player 1 in the special case v 1 > v 2 = v 3 = … = v n .

Suggested Citation

  • Ilan Adler & Yang Cao & Richard Karp & Erol A. Peköz & Sheldon M. Ross, 2017. "Random Knockout Tournaments," Operations Research, INFORMS, vol. 65(6), pages 1589-1596, December.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:6:p:1589-1596
    DOI: 10.1287/opre.2017.1657
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    References listed on IDEAS

    as
    1. 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.
    2. Jeff Horen & Raymond Riezman, 1985. "Comparing Draws for Single Elimination Tournaments," Operations Research, INFORMS, vol. 33(2), pages 249-262, April.
    3. Sheldon H. Jacobson & Douglas M. King, 2009. "Seeding in the NCAA Men's Basketball Tournament: When is a Higher Seed Better?," Journal of Gambling Business and Economics, University of Buckingham Press, vol. 3(2), pages 63-87, September.
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    Cited by:

    1. Federico Della Croce & Gabriele Dragotto & Rosario Scatamacchia, 2022. "On fairness and diversification in WTA and ATP tennis tournaments generation," Annals of Operations Research, Springer, vol. 316(2), pages 1107-1119, September.

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