Matching Japanese Doctors: problems with the current mechanisms, and suggestions for improvement by Yuichiro Kamada and Fuhito Kojima

How to get more doctors into rural hospitals? That's a problem that confronts Japanese medical administrators, and American ones too. Apparently the Japanese Ministry of Health, Labor and Welfare has somewhat more control over the medical labor market than is available in the U.S., since they have instituted regional caps on how many new doctors--residents--can be assigned to urban regions.

But the way that they have implemented these caps, and integrated them with the job market for Japanese medical residents, isn't efficient. This is pointed out in a new paper which also proposes and analyzes an alternative design with more appealing properties. (A related paper also considers a simpler fix for the problem, and discusses why this wouldn't quite work...). Here's the new paper:
Improving Efficiency in Matching Markets with Regional Caps: The Case of the Japan Residency Matching Program by Yuichiro Kamada and Fuhito Kojima), December 2010. (Revise and Resubmit, American Economic Review.

(A non-technical introduction to this paper (in Japanese) is here (written by Yuichiro Kamada, Fuhito Kojima and Jun Wako), and here's a short summary in English, which also discusses why a simple fix--an "iterated deferred acceptance algorithm"-- wouldn't be strategy proof for doctors): Stability and Strategy-Proofness for Matching with Constraints: A Problem in the Japanese Medical Matching and Its Solution by Yuichiro Kamada and Fuhito Kojima, September 2011, Forthcoming, American Economic Review Papers and Proceedings.)

Here's the Abstract: "In an attempt to increase the placement of medical residents in rural hospitals, the Japanese government recently introduced "regional caps" which restrict the total number of residents matched within each region of the country. To accommodate regional caps, the government modified the deferred acceptance mechanism in a particular manner. Motivated by this policy change, we study the design of matching markets under constraints on doctor distribution. This paper shows that the Japanese mechanism may result in avoidable inefficiency and instability and proposes a better mechanism that improves upon it in terms of efficiency and stability while respecting the regional caps."

The inefficiency that they observe occurs arises because of the way the regional cap is translated into caps on the number of residents that can be hired by individual hospitals in the region. If the regional cap is to be, say, 75% of the total of the regional hospitals' original capacity to receive new residents in the Japanese Medical Resident Matching Program (JRMP), then each hospital's individual capacity is set to be .75 of its original capacity. The inefficiency arises when some hospitals fail to fill all of their capacity defined in this way, while other hospitals, which have filled their new, artificially low capacity, are prevented from hiring extra residents even though they could do so without violating the cap on the number of residents allowed in the region. These hospitals could even be part of blocking pairs that would not violate the regional caps, i.e.the outcome would be unstable even under an appropriately defined notion of stability with regional caps.

The JRMP uses a doctor-proposing deferred acceptance algorithm (like the U.S. NRMP, although apparently without the many match variations involved in the American match.) One way proposed to fix the problem described above would be to run the deferred acceptance algorithm once, and if some hospitals in a region had empty positions, allow these to revert back to other hospitals in the region and run the JRMP again. Yuichiro and Fuhito observe that this iterated deferred acceptance algorithm wouldn't be strategy-proof for doctors: it might give doctors incentives to truncate the preference lists they submit.

Instead, they observe that each proposed matching determines not only an assignment of residents to hospitals, but also, for each region, a vector of how many residents have been assigned to each of the region's hospitals. If this vector is evaluated according to some "regional preference relation" over vectors that obeys the substitutes property, then a notion of "stability under regional preferences" can be defined that allows many of the recent results from the literature on matching with contracts to be applied. (An example of a regional preference with the substitutes property would be to prefer vectors in which hospitals were closer to having proportional caps to those in which some hospitals received disproportionately more residents than others.)

They propose what they call a (doctor-proposing) Flexible Deferred Acceptance Algorithm, which allows hospitals to more flexibly determine how many residents to hire, while respecting the regional caps. The way it works is that, after a conventional doctor-proposing step of the deferred acceptance algorithm, each region selects its most preferred feasible vector of capacities, and hospitals in each region choose their choice sets with respect to this capacity, and reject only those applicants who aren't chosen under this capacity. It produces an outcome that is both stable under regional preferences and strategy proof for doctors.

It looks like it could be put to use in Japan in the years to come.

Yuichiro is an already-widely published game theorist with broad interests, mostly in more classical kinds of game theory. His papers are here. You could hire him this year.