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Near-Feasible Stable Matchings with Couples
1Krannert School of Management, Purdue University, 403 W. State Street, West Lafayette, IN 47906.
The American Economic Review
|October 31, 2018
Summary
Stable matching for medical residents is complex, especially for couples. This study shows that a stable matching can be found by slightly adjusting hospital capacities, ensuring fairness in the National Resident Matching program.
Area of Science:
- Algorithmic game theory
- Matching theory
- Medical education logistics
Background:
- The National Resident Matching program aims for stable assignments of medical students to hospitals.
- Stable matchings are not guaranteed to exist, particularly in scenarios involving couples.
Purpose of the Study:
- To demonstrate the existence of a stable matching for any given instance of the medical matching problem.
- To introduce a method for achieving stability by modifying hospital capacities.
Main Methods:
- Investigating the theoretical properties of stable matching algorithms.
- Introducing a perturbation method to adjust hospital capacities.
- Analyzing the bounds of capacity adjustments.
Main Results:
- For any set of student preferences, a nearby instance with a stable matching always exists.
- This stable instance is achieved by perturbing hospital capacities.
- Capacity adjustments are minimal: aggregate capacity increases by at most four, and individual hospital capacities change by no more than two.
Conclusions:
- The National Resident Matching program can always achieve a stable matching through minor, bounded adjustments to hospital capacities.
- This approach ensures a more robust and stable matching process, even with complex preferences like those of couples.
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