Incentive compatible designs for FIFA and UEFA tournament qualifiers

Tournament organisers supposedly design rules such that a team cannot be better off by exerting a lower effort. It is shown that the European qualifiers to the 2018 FIFA World Cup do not satisfy this requirement: a team might be eliminated if it wins its last match in the group stage, while it advances to the next qualification round by playing a draw, provided that all other results remain the same. We present a theoretical model and identify nine incentive incompatible qualifiers to the recent FIFA World Cups and UEFA European Championships. Two mechanisms are suggested in order to prevent manipulation in similar group-based qualification systems where teams from different groups should be compared in a repechage. The first is based on abolishing the anonymity of the matches discarded in the repechage, while the second involves a rethinking of the seeding procedure.