On Stable and Efficient Mechanisms for Priority-based Allocation Problems

Associate Professor, Shanghai University of Finance and Economics

Prof. Zhang's CV.

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, independent 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 always produces a complete assignment if and only if the associated deferred acceptance algorithm is Pareto efficient, or equivalently, if and only if the priority structure is acyclic. Furthermore, for any such priority structure, the assignment made by iteratively removing TFS coincides with that of the deferred acceptance algorithm.