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Strategic manipulation in tournament games

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  • Vong, Allen I.K.

Abstract

I consider the strategic manipulation problem in multistage tournaments. In each stage, players are sorted into groups in which they play pairwise matches against each other. The match results induce a ranking over players in each group, and higher ranked players qualify to the next stage. Players prefer qualifying to higher stages. In this setting, a player may potentially profit by exerting zero effort in some matches even when effort exertion is costless. Since such behavior manipulates the tournament, it is desired that full effort exertion is an equilibrium and any equilibrium ranking of qualifying players is immune to manipulation. To this end, I show that it is both necessary and sufficient to allow only the top-ranked player to qualify from each group. Otherwise, rankings can become a noisy indicator of players' strengths, while effort cost and heterogeneous prize spread can be of little relevance to players' effort choices.

Suggested Citation

  • Vong, Allen I.K., 2017. "Strategic manipulation in tournament games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 562-567.
    • Handle: RePEc:eee:gamebe:v:102:y:2017:i:c:p:562-567
    DOI: 10.1016/j.geb.2017.02.011
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    Cited by:

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    2. Krumer, Alex & Megidish, Reut & Sela, Aner, 2023. "Strategic manipulations in round-robin tournaments," Mathematical Social Sciences, Elsevier, vol. 122(C), pages 50-57.
    3. Csató, László, 2019. "A note on the UEFA Euro 2020 qualifying play-offs," MPRA Paper 93006, University Library of Munich, Germany.
    4. 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.
    5. Arlegi, Ritxar & Dimitrov, Dinko, 2020. "Fair elimination-type competitions," European Journal of Operational Research, Elsevier, vol. 287(2), pages 528-535.
    6. Hall Nicholas G. & Liu Zhixin, 2024. "Opponent choice in tournaments: winning and shirking," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 20(2), pages 67-86, June.
    7. 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.
    8. László Csató, 2022. "How to design a multi-stage tournament when some results are carried over?," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(3), pages 683-707, September.
    9. Muhammad Asif & Ali Ahmadian & Muhammad Azeem & Bruno Antonio Pansera, 2021. "A short comparative study on modified Duckworth-Lewis methods," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-12, November.
    10. 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.
    11. László Csató, 2020. "The UEFA Champions League seeding is not strategy-proof since the 2015/16 season," Annals of Operations Research, Springer, vol. 292(1), pages 161-169, September.
    12. Csató, László & Petróczy, Dóra Gréta, 2022. "Hogyan számszerűsíthető az ösztönzéskompatibilitás? Esettanulmány a sport világából [Quantifying incentive compatibility: a case study from the world of sports]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 841-852.
    13. Csató, László, 2017. "European qualifiers to the 2018 FIFA World Cup can be manipulated," MPRA Paper 82652, University Library of Munich, Germany.
    14. 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.
    15. Robertson, Matthew J., 2018. "Contests with Ex-Ante Target Setting," CRETA Online Discussion Paper Series 47, Centre for Research in Economic Theory and its Applications CRETA.
    16. László Csató, 2021. "A comparison of penalty shootout designs in soccer," 4OR, Springer, vol. 19(2), pages 183-198, June.
    17. Csató, László & Petróczy, Dóra Gréta, 2018. "Néhány gondolat a labdarúgás rangsorolási szabályairól a 2018. évi labdarúgó-világbajnokság európai selejtezője kapcsán [Some ideas on ranking rules in association football in the light of the Euro," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 632-649.
    18. László Csató, 2019. "UEFA Champions League Entry Has Not Satisfied Strategyproofness in Three Seasons," Journal of Sports Economics, , vol. 20(7), pages 975-981, October.
    19. Csató, László, 2022. "Quantifying incentive (in)compatibility: A case study from sports," European Journal of Operational Research, Elsevier, vol. 302(2), pages 717-726.
    20. Csató, László, 2017. "Tournaments with subsequent group stages are incentive incompatible," MPRA Paper 83269, University Library of Munich, Germany.
    21. Marta Boczoń & Alistair J. Wilson, 2023. "Goals, Constraints, and Transparently Fair Assignments: A Field Study of Randomization Design in the UEFA Champions League," Management Science, INFORMS, vol. 69(6), pages 3474-3491, June.

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    More about this item

    Keywords

    Tournament design; Contest design; Strategic manipulation; Subgame perfect implementation; Incentive-compatibility;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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