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The structure, efficacy, and manipulation of double-elimination tournaments

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  • Stanton Isabelle

    (Google Inc, 1600 Amphitheatre Parkway, Mountain View, CA 94043, USA Computer Science Department, Stanford University, 353 Serra Mall, Stanford, CA 94305, USA)

  • Williams Virginia Vassilevska

    (Computer Science Department, Stanford University, 353 Serra Mall, Stanford, CA 94305, USA)

Abstract

A double-elimination tournament is a competition where no participant is eliminated until they have lost two matches. It is structured as two single-elimination tournaments: the winner bracket and the loser bracket. Players who lose once in the winner bracket are mapped to positions in the loser bracket, according to a mapping called the link function. Surprisingly, although the same structure of the winner and loser brackets is used universally, there is no standard definition of the link function. By investigating several design goals, we show that the functions used in practice are not optimal. We propose a similar function that is optimal with respect to our design goals. In order to demonstrate some of the possible research questions about double-elimination tournaments, we address the manipulability of the outcome of a double-elimination tournament. We show that they are vulnerable to manipulation by a coalition of players who can improve their chance of winning by throwing matches, a phenomenon recently observed in Olympic Badminton. We also discuss the computational complexity of manipulation by a tournament organizer (agenda control) in two settings: by changing the player seeding in the winner bracket, or by picking the mapping of losers to the loser bracket. We provide algorithms, hardness proofs, and we formulate open problems for future research.

Suggested Citation

  • Stanton Isabelle & Williams Virginia Vassilevska, 2013. "The structure, efficacy, and manipulation of double-elimination tournaments," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 9(4), pages 319-335, December.
    • Handle: RePEc:bpj:jqsprt:v:9:y:2013:i:4:p:319-335:n:3
    DOI: 10.1515/jqas-2012-0055
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    References listed on IDEAS

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    1. 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.
    2. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    3. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
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    Cited by:

    1. Eric Mao, 2023. "The Incentive Effects of Tournaments and Peer Effects in Team Production: Evidence from Esports," Journal of Sports Economics, , vol. 24(2), pages 174-192, February.

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