Near Feasible Stable Matchings with Complementarities

Thanh Nguyen () and Rakesh Vohra ()
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Thanh Nguyen: Krannert School of Management, Purdue University
Rakesh Vohra: Department of Economics, University of Pennsylvania

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

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 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 (search for similar items in EconPapers)
JEL-codes: C78 D47 (search for similar items in EconPapers)
Pages: 52 pages
Date: 2014-08-01
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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