I attended a lunch

seminar on microeconomics at University of Tokyo today (May 27th);

**Fuhito Kojima**, one of the most productive game theorists in my ages, talked about his recent matching paper with

**Yuichiro Kamada** (a rising star at Harvard):

"Improving Efficiency in Matching Markets with Regional Caps: The Case of the Japan Residency Matching Program" (joint with Yuichiro Kamada)

Their work is strongly motivated by the actual centralized matching system used in the

**Japan residency matching program (JRMP)**. JRMP, as it follows

**NRMP** in the U.S., employs the

**Gale-Shapley algorithm** to assign doctors to hospitals. However, due to the vacancy problem at (mainly) rural hospitals, JRMP recently introduced

**"regional caps"** to each prefecture in order to control the numbers of doctors in popular area.

The current paper theoretically investigates the effects of imposing such an exogenous caps to the GS algorithm. Based on the

**new stability concept** they define, which incorporates regional cap constraints in a natural way and coincides with the usual stability if there were no caps, they show the followings:

- The current Japanese mechanism, i.e., exogenous regional caps + GS, is
**not a stable matching** mechanism.
- There exists a new algorithm (natural extension of the GS) that always a
**stable** and **constrained efficient** matching.
- This new mechanism is
**group strategy-proof** for doctors, that is, any group of doctors does not have an incentive to manipulate their preferences.

Here is a technical remark. To define new algorithm, we have to decide two things (which are absent from the usual GS algorithm), (1)

**target caps** and (2) an

**order of hospitals**. As I remember correctly, the resulting outcome is independent of the choice of (1) (whenever target caps satisfy weak feasibility conditions), but the speaker didn't mention whether the outcome is also invariant to (2) or not. I may better ask him later...

I found the paper really interesting: motivation is clear, results look nice, contains important policy implication, can be applied to different matching problems, and so on. It might be desirable if they could provide some policy recommendation with respect to the choice of regional caps. Although actual caps are typically determined by politics or something other than economic theory I suppose, some benchmark analysis should be helpful. Anyways, I like this paper very much :) (We may perhaps find its title on the front page of some top journal in the near future!)