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Sequential round-robin tournaments with multiple prizes

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  • Laica, Christoph
  • Lauber, Arne
  • Sahm, Marco

Abstract

We examine the fairness and intensity of sequential round-robin tournaments with multiple prizes and heterogeneous players. A tournament is called fair if the winning probabilities in each match depend only on the players' characteristics but not on the sequence of matches. We show that tournaments with three players will be fair if and only if the second prize is valued half of the first prize. The optimal prize structure may, however, be subject to a trade-off between fairness and intensity (measured by the players' expected aggregate effort). By contrast, there is no prize structure for which tournaments with more than three players will be fair if the sequence of matches is exogenously fixed. Our analysis suggests that many tournaments of major sporting events are inherently unfair.

Suggested Citation

  • Laica, Christoph & Lauber, Arne & Sahm, Marco, 2021. "Sequential round-robin tournaments with multiple prizes," Games and Economic Behavior, Elsevier, vol. 129(C), pages 421-448.
    • Handle: RePEc:eee:gamebe:v:129:y:2021:i:c:p:421-448
    DOI: 10.1016/j.geb.2021.06.012
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    Cited by:

    1. Deren Çağlayan & Emin Karagözoğlu & Kerim Keskin & Çağrı Sağlam, 2022. "Effort comparisons for a class of four-player tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(1), pages 119-137, July.
    2. Dmitry Dagaev & Andrey Zubanov, 2022. "Round-robin tournaments with limited resources," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 525-583, October.
    3. Chen Cohen & Ishay Rabi & Aner Sela, 2023. "Optimal seedings in interdependent contests," Annals of Operations Research, Springer, vol. 328(2), pages 1263-1285, September.
    4. Fabian Dietz & Marco Sahm, 2024. "Fairness in Round-Robin Tournaments with Four Players and Endogenous Sequences," CESifo Working Paper Series 11145, CESifo.
    5. Lauber, Arne & March, Christoph & Sahm, Marco, 2023. "Optimal and fair prizing in sequential round-robin tournaments: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 141(C), pages 30-51.

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    More about this item

    Keywords

    Round-robin tournament; Multiple prizes; Fairness; Intensity; Tullock contest; All-pay auction;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • Z20 - Other Special Topics - - Sports Economics - - - General

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