School Choice with General Constraints: A Market Design Approach for the Nursery School Waiting List Problem in Japan

Abstract

This study considers a school choice problem with general feasibility constraints. Each student belongs to a grade; and 2 students belonging to the same grade are symmetric, whereas those belonging to different grades can be asymmetric with respect to the feasibility constraint of a school. We introduce five requirements of a matching and a polynomial‐time algorithm to derive a matching satisfying them. Because the algorithm is inspired by the nursery school system of Yokohama City, we introduce the system and compare it with the algorithm of this study.

Daycare Matching in Japan: Transfers and Siblings

“…A possible approach is to establish flexible quotas instead of hard targets that comply with two feasibility regulations imposed by the government. As shown in two recent work (Okumura 2019;Kamada and Kojima 2019), flexible quotas could significantly increase the number of matched children.…”

“…We next give a brief description of related work (a more detailed literature review is presented in Appendix 3 ). Two previous works on the Japanese daycare matching problem study flexible quotas instead of hard quotas and do not consider transfers and siblings (Okumura 2019;Kamada and Kojima 2019). There exists rich literature on hospital-doctor matching with couples (Kojima, Pathak, and Roth 2013;Biró, Manlove, and McBride 2014;Manlove, McBride, and Trimble 2017;Nguyen and Vohra 2018), which is different from our setting as described in Introduction.…”

Stable Matchings in Practice: A Constraint Programming Approach

“…On the other hand, two recent papers delve into school choice with siblings, but assuming restrictive preferences of families (Dur, Morrill, and Phan 2022;Correa et al 2022). Regarding the Japanese daycare matching problem, two prior works investigate transferable quotas but do not consider initial enrollments or siblings in their models (Okumura 2019;Kamada and Kojima 2023). Another study also examines the Japanese daycare matching market; however, they do not allow for transferable quotas and propose an algorithm suitable for a specific scenario with a maximum of three children per family (Sun et al 2023).…”