The Day Care Assignment: A Dynamic Matching Problem

Abstract

We study the problem of centralized allocation of children to public day care centers, illustrated by the case of Denmark. Our framework applies to problems of dynamic matching in which there is entry and exit of agents over time; for example, the school choice problem once student mobility is taken into account. We show that there does not exist any mechanism that is both stable and strategy-proof. We also show that the well-known Top Trading Cycles mechanism is neither Pareto efficient nor strategy-proof. Finally, a mechanism in which parents sequentially choose menus of schools is both strategy-proof and Pareto efficient. (JEL C73, D82, I21)

Centralized allocation in multiple markets

“…For example, Kennes et al (2012) suggest the use of a mechanism which is a variation of the sequential dictatorship for the dynamic problem of allocating children to public daycares.…”

“…An example is the allocation of new physicians in the United Kingdom, where each young doctor applies to two successive positions -a medical post and a surgical post (Roth, 1991;Irving, 1998). Another example of multiple market allocation is the assignment of young children to public daycares (Kennes et al, 2012). A simple, illustrative, example is the allocation of courses among the faculty of a department in which each professor teaches one course per semester.…”

Efficiency and fair access in Kindergarten allocation policy design

“…they should have the highest priority in their current Kindergarten. This question has been studied in the context of Danish daycare allocation (Kennes et al, 2014), and also for the reallocation of French teachers (Combe et al, 2015).…”

Practical Application of Matchmaking Problem: Trainee Allocation for Teachers

“…In the daycare system in Denmark [4], priorities are imposed by local municipality (e.g. all schools give priority to their currently enrolled children and to the children with special needs).…”

“…Many real-world problems can be understood as matchmaking problems in which two sets need to be paired up: the assignment of junior physicians to hospitals [1], staff to faculties [2], students to colleges [3], children to schools [1,4], online matrimony [5], etc. Whatever the application domains are, the problem consists in finding the best matching between individuals.…”