Stable many-to-many matchings with contracts |
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Authors: | Bettina Klaus Markus Walzl |
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Institution: | aHarvard Business School, Baker Library, Bloomberg Center 437, Soldier Field, Boston, MA 02163, USA;bDepartment of Economics, Bamberg University, Feldkirchenstr. 21, 96045 Bamberg, Germany |
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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. |
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Keywords: | Many-to-many matching Matching with contracts Pairwise stability Setwise stability |
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