Near Feasible Stable Matchings with Complementarities

52 Pages Posted: 25 Sep 2014 Last revised: 21 May 2018

See all articles by Thanh Nguyen

Thanh Nguyen

Purdue University - Krannert School of Management

Rakesh Vohra

University of Pennsylvania - Department of Economics

Date Written: August 1, 2014

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 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 h satisfying [kh–k¹h] ≤ 4 for all hospital h, and h kh ≤ ∑ k¹h ≤ ∑h kh 9, such that a stable matching exists with respect to . 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

Nguyen, Thanh and Vohra, Rakesh, Near Feasible Stable Matchings with Complementarities (August 1, 2014). PIER Working Paper No. 14-028. Available at SSRN: https://ssrn.com/abstract=2500824 or http://dx.doi.org/10.2139/ssrn.2500824

Thanh Nguyen

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

Rakesh Vohra (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

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