Abstract
We propose a notion of core for school choice (i.e., priority-based allocation) problems. We say that a coalition of students is able to enforce a subassignment among them if, given their priorities at schools, other students together cannot exclude any student in the coalition from her assigned school. An assignment is in the core if no coalition of students can enforce any subassignment among them that Pareto improves their assignments. We show that all assignments in the core are Pareto efficient, and the assignment produced by Kesten’s efficiency-adjusted deferred acceptance algorithm is always in the core. We also propose a natural refinement of the core and show that it is equivalent to the concept of priority-efficiency proposed by Reny (Am Econ Rev 112:2025–2043, 2022).
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We are grateful to the Editor Nicholas Yannelis and two anonymous referees for comments and suggestions that greatly improve the paper. We thank Ning Sun, Xiang Sun, Yu Zhou, and paticipants at Tsinghua University, The University of Macau, the 2020 Nanjing-Osaka Economic Theory Workshop, the 2020 Conference on Mechanism and Institution Design, and the SAET 2021 Annual Conference for helpful comments and discussions. This project is supported by National Natural Science Foundation of China (No. 72273085, No. 71873081, and No. 72033004).
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Rong, K., Tang, Q. & Zhang, Y. The core of school choice problems. Econ Theory 77, 783–800 (2024). https://doi.org/10.1007/s00199-023-01507-y
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DOI: https://doi.org/10.1007/s00199-023-01507-y