ABSTRACT 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.

中文翻译：

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基于群体的资格制度的激励（不）兼容性

摘要 比赛组织者应该设计规则，这样一个团队不会因为付出较少的努力而变得更好。然而，众所周知，最近国际足联足球世界杯的欧洲资格赛违反了这一要求，这激发了我们对类似的基于团体的资格制度的激励兼容性的研究。提供了列出策略证明的充分必要条件的定理，并将其应用于对 FIFA 世界杯和 UEFA 欧洲锦标赛的几个足球资格赛进行分类。针对激励不相容的问题，提出了两种合理的机制：第一种是基于取消不同组队比较中丢弃的比赛的匿名性，第二种是重新思考种子程序。