Stable Many-to-Many Matchings with Contracts

Klaus, Bettina-Elisabeth; Walzl, Markus

doi:10.2139/ssrn.1273622

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Stable Many-to-Many Matchings with Contracts

Harvard Business School NOM Working Paper No. 09-046

25 Pages Posted: 28 Sep 2008 Last revised: 14 May 2009

See all articles by Bettina-Elisabeth Klaus

Markus Walzl

Free University of Bozen-Bolzano

Date Written: September 25, 2008

Abstract

We consider several notions of setwise stability for many-to-many matching markets with contracts and provide an analysis of the relations between the resulting sets of stable allocations for general, substitutable, and strongly substitutable preferences. Apart from obtaining "set inclusion results" on all three domains, we introduce weak setwise stability as a new stability concept and prove that for substitutable preferences the set of pairwise stable matchings is nonempty and coincides with the set of weakly setwise stable matchings. For strongly substitutable preferences the set of pairwise stable matchings coincides with the set of setwise stable matchings.

Keywords: Many-to-Many Matching, Matching with Contracts, Pairwise Stability, Setwise Stability

JEL Classification: C62, C78, D78, J41

Suggested Citation: Suggested Citation

Klaus, Bettina-Elisabeth and Walzl, Markus, Stable Many-to-Many Matchings with Contracts (September 25, 2008). Harvard Business School NOM Working Paper No. 09-046, Available at SSRN: https://ssrn.com/abstract=1273622 or http://dx.doi.org/10.2139/ssrn.1273622