New axioms for top trading cycles

TL;DR

This paper introduces new axioms to analyze the student-optimal top trading cycles mechanism in school choice, providing a novel axiomatic characterization and comparison with other mechanisms under various priority structures.

Contribution

It proposes two new axioms, MBG-quota-rationality and MBG-robust efficiency, and characterizes the TTCM using these axioms, enhancing understanding of its properties and comparisons.

Findings

TTCM is characterized by MBG-quota-rationality and MBG-robust efficiency.

MBG-robust efficiency is weaker than robust efficiency but stronger than efficiency plus group strategy-proofness.

Results offer a new basis for comparing TTCM with other school choice mechanisms.

Abstract

School choice 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, especially the student-optimal stable mechanism under Ergin but not Kesten-acyclic priority structures.