Matching of like rank and the size of the core in the marriage problem

• 成果类型: Article
• 署名作者: Holzman, Ron; Samet, Dov
• 署名单位: Technion Israel Institute of Technology; Tel Aviv University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2014.10.003
• 发表日期: 2014
• 页码: 277-285
• 关键词: marriage problem; stable matching; core; Correlated preferences; assortative matching

摘要

When men and women are objectively ranked in a marriage problem, say by beauty, then pairing individuals of equal rank is the only stable matching. We generalize this observation by providing bounds on the size of the rank gap between mates in a stable matching in terms of the size of the ranking sets. Using a metric on the set of matchings, we provide bounds on the diameter of the core - the set of stable matchings - in terms of the size of the ranking sets and in terms of the size of the rank gap. We conclude that when the set of rankings is small, so are the core and the rank gap in stable matchings. We construct examples showing that our bounds are essentially tight, and that certain natural variants of the bounds fail to hold. (C) 2014 Elsevier Inc. All rights reserved.