Near Feasible Stable Matchings with Complementarities
52 Pages Posted: 25 Sep 2014 Last revised: 21 May 2018
Date Written: August 1, 2014
The National Resident Matching program strives for a stable matching of medical students to teaching hospitals. With the presence of couples, stable matchings need not exist. For any student preferences, we show that each instance of a stable matching problem has a ’nearby’ instance with a table matching. The nearby instance is obtained by perturbing the capacities of the hospitals. Specifically, given a reported capacity kh ( for each hospital h, we find a redistribution of the slot capacities k¹h satisfying [kh–k¹h] ≤ 4 for all hospital h, and ∑h kh ≤ ∑ k¹h ≤ ∑h kh 9, such that a stable matching exists with respect to k¹. Our approach is general and applies to other type of complementarities, as well as matchings with side constraints and contracts.
Keywords: stable matching, complementarities, Scarf's lemma
JEL Classification: C78, D47
Suggested Citation: Suggested Citation