On the extent of collusion created by tie-breaking rules

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.