Large roommate problem with non-transferable random utility

• 成果类型: Article
• 署名作者: Peski, Marcin
• 署名单位: University of Toronto
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2016.12.012
• 发表日期: 2017
• 页码: 432-471
• 关键词: Matching; random utility; Large market

摘要

We analyze a large roommate problem (i.e., marriage matching in which the marriage is not restricted solely to matchings between men and women) with non-transferable utility. It is well known that while a roommate problem may not have a stable proper matching, each roommate problem does have an stable improper matching. In a random utility model with types from Dagsvik (2000) and Menzel (2015), we show that all improper stable matchings are asymptotically close to being a proper stable matching. Moreover, the distribution of types in stable matchings (proper or not) converges to the unique maximizer of an expression that is a sum of two terms: the average welfare of the matching and the Shannon entropy of the distribution. In the noiseless limit, when the random component of the utility is reduced to zero, the distribution of types of matched pairs converges to the outcome of the transferable utility model. Crown Copyright (C)2017 Published by Elsevier Inc. All rights reserved.