We consider school choice problems (Abdulkadiroğlu and Sönmez, 2003) where students are assigned to public schools through a centralized assignment mechanism. We study the family of so-called rank-priority mechanisms, each of which is induced by an order of rank-priority pairs. Following the corresponding order of pairs, at each step a rank-priority mechanism considers a rank-priority pair and matches an available student to an unfilled school if the student and the school rank and prioritize each other in accordance with the rank-priority pair. The Boston or immediate acceptance mechanism is a particular rank-priority mechanism. Our first main result is a characterization of the subfamily of rank-priority mechanisms that Nash implement the set of stable matchings (Theorem 1). Our second main result is a strong impossibility result: under incomplete information, no rank-priority mechanism implements the set of stable matchings (Theorem 2).

我们考虑学校选择问题（Abdulkadiroğlu 和 Sönmez，2003 年），其中学生通过集中分配机制被分配到公立学校。我们研究了所谓的等级优先级机制家族，每个机制都是由等级优先级对的顺序引起的。按照对的相应顺序，在每一步，排名优先机制都会考虑排名优先对，如果学生和学校根据排名优先对彼此排名和优先顺序，则排名优先机制将可用学生与空缺学校匹配。波士顿或立即接受机制是一种特殊的等级优先机制。我们的第一个主要结果是对 Nash 实现稳定匹配集（定理 1）的等级优先机制子族的表征。我们的第二个主要结果是一个很强的不可能结果：