Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
957753 | Journal of Economic Theory | 2007 | 11 Pages |
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).
Keywords
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Social Sciences and Humanities
Economics, Econometrics and Finance
Economics and Econometrics
Authors
Lars Ehlers,