Improving Fairness and Efficiency in Matching with Distributional Constraints: An Alternative Solution for the Japanese Medical Residency Match

Regional imbalance of doctors is a serious issue in many countries. In an attempt to average the geographical distribution of doctors, the Japanese government introduced ``regional caps'' recently, restricting the total number of medical residents matched within each region. Motivated by this policy change, Kamada and Kojima (2013) proposed a mechanism called the flexible deferred acceptance mechanism (FDA) that makes every doctor weakly better off than the current system. In this paper, we further study this problem and develop an alternative mechanism that we call the priority-list based deferred acceptance mechanism (PLDA). Both mechanisms enable hospitals in the same region to fill their capacities flexibly until the regional cap is filled. FDA lets hospitals take turns to (tentatively) choose the best remaining doctor, while PLDA lets each region directly decide which doctor is (tentatively) matched with which hospital based on its priority list. We show that PLDA performs better than FDA in terms of efficiency and fairness through theoretical and computational analyses.