Yuichiro Kamada, Fuhito Kojima
We consider a school-choice matching model that allows for inter-district transfer of students, with the “balancedness” constraint: each student and school belongs to a region, and a matching is said to be balanced if, for each region, the outflow of students from that region to other regions is equal to the inflow of students from the latter to the former. Using a directed bipartite graph defined on students and schools, we characterize the set of Pareto efficient matchings among those that are individually rational, balanced and fair. We also provide a polynomial-time algorithm to compute such matchings. The outcome of this algorithm weakly improves student welfare upon the one induced when each region independently organizes a standard matching mechanism.