Consistency of the doctor-optimal equilibrium price vector in job-matching markets

• 成果类型: Article
• 署名作者: Yokote, Koji
• 署名单位: Waseda University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2021.105346
• 发表日期: 2021
• 关键词: Job matching; competitive equilibria; comparative statics; strategy-proofness; Discrete convex analysis

摘要

In a many-to-many variation of Kelso and Crawford's (1982) and Kojima et al.'s (2019) job-matching model, we prove that the doctor-optimal equilibrium price vector satisfies a striking property termed con-sistency. It states that the price vector remains an equilibrium price vector in the market where an arbitrary doctor reduces her capacity by one. Combining consistency with Kojima et al.'s (2019) result, we delineate how the set of equilibrium price vectors moves when a doctor reduces her capacity by one: the set moves up but still contains the original doctor-optimal equilibrium price vector. We apply this result to establish comparative statics of welfare at equilibrium. As a byproduct, we also provide a simple and short proof of the claim that the doctor-optimal stable mechanism is a pivotal mechanism under quasi-linear preferences. (c) 2021 Elsevier Inc. All rights reserved.