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The Optimal Design of Round-Robin Tournaments with Three Players

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  • Krumer, Alex
  • Megidish, Reut
  • Sela, Aner

Abstract

We study the optimal design of round-robin tournaments with three symmetric players. We characterize the subgame perfect equilibrium in these tournaments with either one or two prizes. Our results show that the players who wish to maximize their expected payoffs or their probabilities of winning have different preferences about the order of games under tournaments with one or two prizes. We analyze the optimal allocations of players for a designer who wishes to maximize the players' expected total effort in the tournaments with one and two prizes, and by comparing between them, it is demonstrated that in order to maximize the players' expected total effort the designer should allocate only one prize.

Suggested Citation

  • Krumer, Alex & Megidish, Reut & Sela, Aner, 2017. "The Optimal Design of Round-Robin Tournaments with Three Players," Economics Working Paper Series 1713, University of St. Gallen, School of Economics and Political Science.
    • Handle: RePEc:usg:econwp:2017:13
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    References listed on IDEAS

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    8. Alex Krumer & Reut Megidish & Aner Sela, 2017. "First-mover advantage in round-robin tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 633-658, March.
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    20. Dries Goossens & Frits Spieksma, 2009. "Scheduling the Belgian Soccer League," Interfaces, INFORMS, vol. 39(2), pages 109-118, April.
    21. Krumer, Alex & Lechner, Michael, 2016. "First In First Win: Evidence on Unfairness of Round-Robin Tournaments in Mega-Events," Economics Working Paper Series 1611, University of St. Gallen, School of Economics and Political Science.
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    Cited by:

    1. Di Mattia, Alessandro & Krumer, Alex, 2023. "Fewer teams, more games, larger attendance? Evidence from the structural change in basketball's EuroLeague," European Journal of Operational Research, Elsevier, vol. 309(1), pages 359-370.
    2. Christoph Laica & Arne Lauber & Marco Sahm, 2017. "Sequential Round-Robin Tournaments with Multiple Prizes," CESifo Working Paper Series 6685, CESifo.
    3. Krumer, Alex & Megidish, Reut & Sela, Aner, 2023. "Strategic manipulations in round-robin tournaments," Mathematical Social Sciences, Elsevier, vol. 122(C), pages 50-57.
    4. Christian Deutscher & Marco Sahm & Sandra Schneemann & Hendrik Sonnabend, 2019. "Strategic Investment Decisions in Multi-stage Contests with Heterogeneous Players," CESifo Working Paper Series 7474, CESifo.
    5. 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.
    6. László Csató, 2020. "Optimal Tournament Design: Lessons From the Men’s Handball Champions League," Journal of Sports Economics, , vol. 21(8), pages 848-868, December.
    7. 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.
    8. Guajardo, Mario & Krumer, Alex, 2023. "Format and schedule proposals for a FIFA World Cup with 12 four-team groups," Discussion Papers 2023/2, Norwegian School of Economics, Department of Business and Management Science.
    9. Chen Cohen & Ishay Rabi & Aner Sela, 2023. "Optimal seedings in interdependent contests," Annals of Operations Research, Springer, vol. 328(2), pages 1263-1285, September.
    10. Fabian Dietz & Marco Sahm, 2024. "Fairness in Round-Robin Tournaments with Four Players and Endogenous Sequences," CESifo Working Paper Series 11145, CESifo.
    11. 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.
    12. Christian Deutscher & Marco Sahm & Sandra Schneemann & Hendrik Sonnabend, 2022. "Strategic investment decisions in multi-stage contests with heterogeneous players," Theory and Decision, Springer, vol. 93(2), pages 281-317, September.

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    More about this item

    Keywords

    Multi-stage contests; all-pay auctions; first-mover advantage; second-mover advantage; round-robin tournaments;
    All these keywords.

    JEL classification:

    • D00 - Microeconomics - - General - - - General
    • L00 - Industrial Organization - - General - - - General
    • D20 - Microeconomics - - Production and Organizations - - - General
    • Z20 - Other Special Topics - - Sports Economics - - - General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives

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