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AbstractThe 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.