On the extent of collusion created by tie-breaking rules

Games played in the final round of a round-robin contest may inspire collusion and match-fixing if there exists a result allowing both teams to advance. Our paper reveals that using head-to-head records as the primary tie-breaking principle might lead to such situations. We identify all possible cases in a single round-robin tournament with four teams. According to simulations based on the UEFA European Football Championship, merely the misaligned tie-breaking policy increases by about 12 percentage points the probability of a match with a collusion opportunity. The danger can scarcely be mitigated using a static match schedule.