Von Neumann-Morgenstern stable sets in matching problems |
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Authors: | Lars Ehlers |
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Affiliation: | Département de Sciences Économiques and CIREQ, Université de Montréal, C.P. 6128 Succursale Centre Ville, Montréal, Québec H3C 3J7, Canada |
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Abstract: | The following properties of the core of a one-to-one matching problem are well-known: (i) the core is non-empty; (ii) the core is a distributive lattice; and (iii) the set of unmatched agents is the same for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (Von Neumann-Morgenstern) stable sets in one-to-one matching problems. We show that a set V of matchings is a stable set of a one-to-one matching problem only if V is a maximal set satisfying the following properties: (a) the core is a subset of V; (b) V is a distributive lattice; and (c) the set of unmatched agents is the same for all matchings belonging to V. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b), and (c). |
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Keywords: | C78 J41 J44 |
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