足球点球大战的标准设计由于偏向第一个点球的球队而受到了严厉的批评。 这项运动的规则制定机构在2017年决定尝试另一种机制。 尽管新政策的实施已经停滞不前，但学术研究人员最近提出了一些其他改善公平性的设计。 本文提供了7个这样的足球罚球机制的广泛概述，其中之一首先在这里定义。 用三种不同的心理压力数学模型分析了他们的公平性。 我们还考虑了到达突然死亡阶段的可能性，以及设计的复杂性和对策略的敏感性。 有些规则被认为是次等的，因为与较简单的机制相比，它们在公平性方面没有获得实质性的收益。 我们的工作有可能影响那些只选择理论上具有竞争力的设计进行现场试验的决策者，他们可以节省资源。

原文题目：A comprehensive analysis of soccer penalty shootout designs

原文：The standard design of soccer penalty shootouts has received serious criticism due to its bias towards the team that kicks the first penalty. The rule-making body of the sport has decided in 2017 to try an alternative mechanism. Although the adoption of the new policy has stalled, academic researchers have recently suggested some other designs to improve fairness. This paper offers an extensive overview of seven such soccer penalty shootout mechanisms, one of them first defined here. Their fairness are analysed in three different mathematical models of psychological pressure. We also consider the probability of reaching the sudden death stage, as well as the complexity and strategy-proofness of the designs. Some rules are found to be inferior as they do not lead to a substantial gain in fairness compared to simpler mechanisms. Our work has the potential to impact decision-makers who can save resources by choosing only theoretically competitive designs for field experiments.

原文作者：László Csató

原文地址：https://arxiv.org/abs/2004.09225