关于以正面交锋结果作为决胜局以及由此产生的串通机会

IF 1.9 3区工程技术 Q3 MANAGEMENT

IMA Journal of Management Mathematics Pub Date : 2024-07-01 DOI:10.1093/imaman/dpae016

László Csató

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引用次数: 0

摘要

接受：Phil Scarf 一些足球比赛的结果使两支球队都获益，但却牺牲了第三支球队的利益，因为头对头的结果被用来打破平局。受这些例子的启发，我们的数学分析找出了在有四支球队的单循环比赛中，这一特殊排名规则可能导致的所有串通机会。根据一个基于 2024 年欧洲足球锦标赛的模拟模型，仅仅是打破平局的规则，就会将容易出现合谋情况的概率提高 11.5 到 14.8 个百分点。这种风险几乎无法通过静态赛程表来降低。因此，强烈建议赛事组织者选择净胜球作为主要的决胜规则，这与国际足联的官方政策类似。

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On head-to-head results as tie-breaker and consequent opportunities for collusion

Accepted by: Phil Scarf The outcome of some football matches has benefited both teams at the expense of a third team because head-to-head results were used for breaking ties. Inspired by these examples, our mathematical analysis identifies all possible collusion opportunities caused by this particular ranking rule in a single round-robin tournament with four teams. According to a simulation model based on the 2024 UEFA European Football Championship, merely the tie-breaking rule increases the probability of reaching a situation vulnerable to collusion by between 11.5 and 14.8 percentage points. This risk can scarcely be mitigated by a static match schedule. Therefore, tournament organizers are strongly encouraged to choose goal difference as the primary tie-breaking rule, similar to the official policy of FIFA.

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来源期刊

IMA Journal of Management Mathematics OPERATIONS RESEARCH & MANAGEMENT SCIENCE-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The mission of this quarterly journal is to publish mathematical research of the highest quality, impact and relevance that can be directly utilised or have demonstrable potential to be employed by managers in profit, not-for-profit, third party and governmental/public organisations to improve their practices. Thus the research must be quantitative and of the highest quality if it is to be published in the journal. Furthermore, the outcome of the research must be ultimately useful for managers. The journal also publishes novel meta-analyses of the literature, reviews of the "state-of-the art" in a manner that provides new insight, and genuine applications of mathematics to real-world problems in the form of case studies. The journal welcomes papers dealing with topics in Operational Research and Management Science, Operations Management, Decision Sciences, Transportation Science, Marketing Science, Analytics, and Financial and Risk Modelling.