2018 FIFA World Cup qualification can be manipulated

Abstract

In the European section of the 2018 FIFA World Cup qualification, 13 national teams, which are members of the Union of European Football Associations (UEFA), can qualify for the final competition. The 54 teams are divided into nine groups to play home-and-away round-robin matches in 10 matchdays. The winners of each group qualify, while the eight best second-placed teams advance to play-offs such that the four winners of play-offs also qualify. Ranking of second-placed teams differs from ranking in groups since group matches against the sixth-placed team are discarded. It is shown that this feature opens a way for manipulation: it may happen that a team is eliminated if it wins in the last matchday of group stage, but it advances to play-offs by playing a draw, provided that all other results are fixed. An example reveals that this situation might even occur in October 2017, after eight matchdays are already played in the qualification. Furthermore, by adjusting the result of only two matches played before October 2017 with an addition of one goal each, a team can strictly prefer a draw over a win in its last match as the former may advance it to play-offs, but the latter certainly leads to its elimination.