Near Feasible Stable Matchings

Abstract

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 stable matching. The nearby instance is obtained by perturbing the capacities of the hospitals. Our approach is general and applies to other type of complementarities, as well as matchings with side constraints and contracts.