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Fairness in penalty shootouts: Is it worth using dynamic sequences?

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  • L'aszl'o Csat'o
  • D'ora Gr'eta Petr'oczy

Abstract

The sequence of moves in a dynamic team tournament may distort the ex-ante winning probabilities and harm efficiency. This paper compares seven soccer penalty shootout rules that determine the kicking order, from a theoretical perspective. Their fairness is evaluated in a reasonable model of First Mover Advantage. We also discuss the probability of reaching the sudden death stage. In the case of stationary scoring probabilities, dynamic mechanisms are not better than static rules. However, it is worth compensating the second-mover by making it the first-mover in the sudden death stage. Our work has the potential to impact decision-makers who can guarantee fairer outcomes in dynamic tournaments by a carefully chosen sequence of actions.

Suggested Citation

  • L'aszl'o Csat'o & D'ora Gr'eta Petr'oczy, 2020. "Fairness in penalty shootouts: Is it worth using dynamic sequences?," Papers 2004.09225, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2004.09225
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    References listed on IDEAS

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    1. Arrondel, Luc & Duhautois, Richard & Laslier, Jean-François, 2019. "Decision under psychological pressure: The shooter's anxiety at the penalty kick," Journal of Economic Psychology, Elsevier, vol. 70(C), pages 22-35.
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    5. Luc Arrondel & Richard Duhautois & Jean-François Laslier, 2019. "Decision under psychological pressure: The shooter's anxiety at the penalty kick," PSE-Ecole d'économie de Paris (Postprint) halshs-02072860, HAL.
    6. Martin G. Kocher & Marc V. Lenz & Matthias Sutter, 2012. "Psychological Pressure in Competitive Environments: New Evidence from Randomized Natural Experiments," Management Science, INFORMS, vol. 58(8), pages 1585-1591, August.
    7. Luc Arrondel & Richard Duhautois & Jean-François Laslier, 2019. "Decision under psychological pressure: The shooter's anxiety at the penalty kick," Post-Print halshs-02072860, HAL.
    8. Tom P. Vandebroek & Brian T. McCann & Govert Vroom, 2018. "Modeling the Effects of Psychological Pressure on First-Mover Advantage in Competitive Interactions," Journal of Sports Economics, , vol. 19(5), pages 725-754, June.
    9. Ignacio Palacios-Huerta, 2012. "Tournaments, Fairness And The Prouhet-Thue-Morse Sequence," Economic Inquiry, Western Economic Association International, vol. 50(3), pages 848-849, July.
    10. Cohen-Zada, Danny & Krumer, Alex & Shapir, Offer Moshe, 2018. "Testing the effect of serve order in tennis tiebreak," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 106-115.
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