Games played in the last round of a round-robin tournament may inspire match-fixing or tacit collusion if there exists a result allowing both teams to advance. This paper reveals that using head-to-head records as the primary tie-breaking principle might lead to such situations and identifies all possible cases in a single round-robin tournament with four teams. According to our simulations based on the 2016 UEFA European Football Championship, collusion opportunities implied exclusively by the official tie-breaking policy arise with a probability of at least 19%. However, the threat can be partially mitigated by choosing an optimal order of matches.

翻译：在循环赛最后一轮比赛中，若存在能使两队同时晋级的结果，则可能诱发假球或默契共谋。本文揭示，以交锋战绩作为首要决胜原则可能导致此类情况，并识别出四队单循环赛中的所有可能情形。基于2016年欧洲足球锦标赛的仿真结果显示，仅由官方决胜规则引发的共谋机会出现概率至少为19%。然而，通过选择最佳比赛顺序可部分缓解这一威胁。