论文标题
作为打preenbreaker的头对头结果，并带来了勾结的机会
On head-to-head results as tie-breaker and consequent opportunities for collusion
论文作者
论文摘要
一些足球比赛的结果使两支球队受益匪浅，牺牲了第三支球队，因为正面的结果被用于打破领带。受这些示例的启发，我们的数学分析确定了由四支球队的一次圆形巡回赛中的这一特定排名规则造成的所有可能的勾结机会。根据基于2024年UEFA欧洲足球锦标赛的模拟模型，仅罢工规则增加了容易串通局势的可能性在11.5到14.8个百分点之间。静态比赛时间表几乎无法减轻这种风险。因此，强烈鼓励锦标赛组织者选择目标差为主要的抢七规则，类似于FIFA的官方政策。
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 organisers are strongly encouraged to choose goal difference as the primary tie-breaking rule, similar to the official policy of FIFA.
