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The incentive (in)compatibility of group-based qualification systems

Tournament organisers supposedly design rules such that a team cannot be strictly better off by exerting a lower effort. However, the European qualification tournaments for recent FIFA soccer World Cups are known to violate this requirement, which inspires our study on the incentive compatibility of similar group-based qualification systems. Theorems listing the sufficient and necessary conditions of strategy-proofness are provided and applied to classify several soccer qualification tournaments for FIFA World Cups and UEFA European Championships. Two reasonable mechanisms are proposed to solve the problem of incentive incompatibility: the first is based on abolishing the anonymity of the matches discarded in the comparison of teams from different groups, while the second involves a rethinking of the seeding procedure. Our results have useful implications for the governing bodies of major sports.