Matching with Minimal Quota: Case Study of a Student-Supervisor Assignment in a Japanese University

Abstract

TThis paper describes a study of the two-sided matching problem with type-specific maximal and minimal quotas with the deferred acceptance mechanism in a student– supervisor assignment. In this problem, both students and supervisors were classified by type according to their affiliations, and the supervisors set type-specific maximal and minimal quotas. In the proposed mechanism, the maximal quotas were dynamically adjusted to fulfill the minimal quotas. We found that while the mechanism may not be strategy-proof, it eliminates justified envy among students of the same “type,” and it achieved feasibility with a certain distributional constraint. Moreover, if the sum of the ranks of students and supervisors in the final assignment is viewed as a measure of welfare, there is no domination relationship between our mechanism and the deferred acceptance mechanism. As evidence, the paper presents a case study of the proposed mechanism in use at a Japanese university.