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Designing practical and fair sequential team contests: The case of penalty shootouts

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  • Anbarcı, Nejat
  • Sun, Ching-Jen
  • Ünver, M. Utku

Abstract

Economists have long recognized that the effect of move order on outcomes is non-negligible in sequential contests. We study tiebreak mechanisms used in team sports and known as penalty shootouts through a dynamic model. We characterize all order-independent mechanisms where two balanced teams have equal chances to win the shootout whenever they are tied after equal numbers of attempts; thus, move order has no relevance for winning chances. In most sports, such as football and hockey, teams take penalties in a fixed order, known as ABAB, while some tournaments adopted the alternating-order variant, ABBA. We find that these and all other exogenous-order mechanisms – with one exception – are order-dependent in regular rounds. Although ABBA is order independent in sudden-death rounds, ABAB is not. Our theory supports empirical studies linking ABAB to unfair outcomes and multiple equilibria in terms of winning chances of the first- vs. second-kicking teams in different football traditions.

Suggested Citation

  • Anbarcı, Nejat & Sun, Ching-Jen & Ünver, M. Utku, 2021. "Designing practical and fair sequential team contests: The case of penalty shootouts," Games and Economic Behavior, Elsevier, vol. 130(C), pages 25-43.
    • Handle: RePEc:eee:gamebe:v:130:y:2021:i:c:p:25-43
    DOI: 10.1016/j.geb.2021.07.004
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    Cited by:

    1. Nejat Anbarci & Mehmet S Ismail, 2024. "AI-powered mechanisms as judges: Breaking ties in chess," PLOS ONE, Public Library of Science, vol. 19(11), pages 1-17, November.
    2. Karlsson, Niklas & Lunander, Anders, 2022. "The Strategic Jump - The Order Effect on Winning “The Final Three” in Long Jump Competitions," Working Papers 2022:8, Örebro University, School of Business.
    3. Gustavo Bergantiños & Juan D. Moreno-Ternero, 2024. "Axiomatic characterizations of the core and the Shapley value of the broadcasting game," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(3), pages 977-988, September.
    4. Singh, Aaditya & Scarf, Phil & Baker, Rose, 2023. "A unified theory for bivariate scores in possessive ball-sports: The case of handball," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1099-1112.
    5. Mackenzie, Andrew & Komornik, Vilmos, 2023. "Fairly taking turns," Games and Economic Behavior, Elsevier, vol. 142(C), pages 743-764.
    6. Brams, Steven & Ismail, Mehmet S. & Kilgour, Marc, 2023. "Fairer Shootouts in Soccer: The m-n Rule," MPRA Paper 116352, University Library of Munich, Germany.
    7. Steven J. Brams & Mehmet S. Ismail & D. Marc Kilgour, 2023. "Fairer Shootouts in Soccer: The $m-n$ Rule," Papers 2303.04807, arXiv.org.
    8. Steven J. Brams & Mehmet S. Ismail, 2024. "Multi-Tier Tournaments: Matching and Scoring Players," Papers 2407.13845, arXiv.org.

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    JEL classification:

    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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