On Stable and Efficient Mechanisms for Priority-Based Allocation Problems

24 Pages Posted: 30 Nov 2017 Last revised: 19 Feb 2020

See all articles by Kang Rong

Kang Rong

Shanghai University of Finance and Economics - School of Economics

Qianfeng Tang

Shanghai University of Finance and Economics - School of Economics

Yongchao Zhang

Shanghai University of Finance and Economics - School of Economics

Date Written: January 6, 2020

Abstract

For school choice (priority-based allocation) problems, when the priority structure is acyclic, the associated student-proposing deferred acceptance algorithm is Pareto efficient and group strategy-proof (Ergin, 2002). We reveal a hidden iterative removal structure behind such deferred acceptance algorithms. A nonempty set of students is called a top fair set (TFS) if when all students apply to their most preferred schools and all schools accept the best applicants up to their quotas, students in the set are always accepted, regardless of other students’ preferences. We provide an elimination process to find the maximal TFS, if any TFS exists. We show that for any priority structure, iterative removal of TFS is equivalent to the associated deferred acceptance algorithm if and only if the latter is a Pareto efficient mechanism.

Keywords: Deferred Acceptance Algorithm, Pareto Efficiency, School Choice, Stability, Strategy-proofness

JEL Classification: C78, D61, D78, I20

Suggested Citation

Rong, Kang and Tang, Qianfeng and Zhang, Yongchao, On Stable and Efficient Mechanisms for Priority-Based Allocation Problems (January 6, 2020). Available at SSRN: https://ssrn.com/abstract=3077761 or http://dx.doi.org/10.2139/ssrn.3077761

Kang Rong

Shanghai University of Finance and Economics - School of Economics ( email )

777 Guoding Road
Shanghai, 200433
China

Qianfeng Tang (Contact Author)

Shanghai University of Finance and Economics - School of Economics ( email )

777 Guoding Road
Shanghai, 200433
China

Yongchao Zhang

Shanghai University of Finance and Economics - School of Economics ( email )

777 Guoding Road Yangpu D.
Shanghai, Shanghai 200433
China

HOME PAGE: http://zhangyongchao.weebly.com

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