Stability and Strategy-Proofness for Matching with Constraints: A Problem in the Japanese Medical Match and Its Solution

Real matching markets are subject to constraints. For example, the Japanese government introduced a new medical matching system in 2009 that imposes a "regional cap" in each of its 47 prefectures, which regulates the total number of medical residents who can be employed in each region. Based on Kamada and Kojima (2011), this paper studies matching markets with such constraints by examining in great detail the Japanese medical matching market. Specifically, we show that the new system introduced in 2009 has problems in terms of stability and strategy-proofness, and provide an alternative mechanism that does better.