Singles monotonicity and stability in one-to-one matching problems

• 成果类型: Article
• 署名作者: Kasajima, Yoichi; Toda, Manabu
• 署名单位: Waseda University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2023.11.001
• 发表日期: 2024
• 页码: 269-286
• 关键词: One-to-one matching; Own-side singles monotonicity; Other-side singles monotonicity; STABILITY; Consistency; Maskin invariance

摘要

We propose a new axiom called own-side singles monotonicity in one-to-one matching problems between men and women. Suppose that there is an agent who is not matched in a problem. Suppose for simplicity it is a woman. Now in a new problem, we improve (or leave unchanged) her ranking for each man. Own-side singles monotonicity requires that each woman should not be made better off (except for her). If we focus on improving the ranking of an unmatched woman, then the men-optimal stable solution satisfies this property. By contrast, (if the gender of an unmatched agent is not specified), no single-valued solution satisfies own-side singles monotonicity and stability. However, there is a multi-valued solution, the stable solution, that does. We show that the stable solution is the unique solution satisfying weak unanimity, null agent invariance, own-side singles monotonicity, and consistency, where consistency can be replaced by Maskin invariance.