The solution
To push doctors into underserved rural areas, Japan's residency matching introduced 'regional caps' limiting how many residents each of the 47 prefectures could employ, and the government modified its deferred acceptance algorithm to incorporate them.
Kamada and Kojima showed the modified system was neither stable nor strategy-proof: doctors could gain by truncating the preference lists they submitted, and acceptable assignments could be blocked. They designed an alternative — flexible deferred acceptance — that respects the caps while restoring stability under regional preferences and strategy-proofness for doctors.
The proposal was circulated in 2010, described by Alvin Roth as a fix that could be put to use in Japan, and published in the American Economic Review in 2012. It became a reference result for matching markets with distributional constraints, a class of problems that appears in school choice, public housing and medical matches.
What it achieved
Keep stability and strategy-proofness under caps
Why it worked
An ad-hoc cap created gaming incentives; flexible DA removes them without abandoning the policy goal.
Stability under regional preferences keeps rural-posting goals compatible with honest ranking.
The analysis generalized to any matching market with quota-like constraints.
What can be applied
When you add a constraint to a well-functioning market, the fix has to be inside the mechanism, not bolted on — an ad-hoc cap on a clean algorithm quietly destroys the incentives you relied on.
Aftermath
The AER paper anchored a research agenda on matching with constraints and became the standard reference for constrained residency matches. The flexible DA mechanism now appears in textbooks and policy discussions wherever regional quotas are imposed on centralized matches.
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