The school choice problem is of great importance both in theory and practice. This paper studies the (student-optimal) top trading cycles mechanism (TTCM) in an axiomatic way. We introduce two new axioms: MBG (mutual best group)-quota-rationality and MBG-robust efficiency. While stability implies MBG-quota rationality, MBG-robust efficiency is weaker than robust efficiency, which is stronger than the combination of efficiency and group strategy proofness. The TTCM is characterized by MBG-quota rationality and MBG-robust efficiency. Our results construct a new basis to compare the TTCM with the other school choice mechanisms, in terms of both fairness and incentive-related axioms.

中文翻译：

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顶级交易周期的新公理

择校问题无论在理论上还是在实践上都具有重要意义。本文以公理化的方式研究了（学生最优）顶部交易周期机制（TTCM）。我们引入两个新公理：MBG（互最佳群体）-配额理性和MBG-鲁棒效率。虽然稳定性意味着MBG配额合理性，但MBG鲁棒效率弱于鲁棒效率，鲁棒效率强于效率和群体策略证明性的组合。TTCM的特点是MBG配额合理性和MBG鲁棒效率。我们的结果构建了一个新的基础，在公平性和激励相关公理方面将 TTCM 与其他择校机制进行比较。