Von Neumann-Morgenstern stable sets in matching problems

• 成果类型: Article
• 署名作者: Ehlers, Lars
• 署名单位: Universite de Montreal; Universite de Montreal
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2006.03.006
• 发表日期: 2007
• 页码: 537-547
• 关键词: Matching problem; von Neumann-Morgenstern stable sets

摘要

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). (c) 2006 Elsevier Inc. All rights reserved.