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

Yoichi Kasajima () and Manabu Toda ()
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Yoichi Kasajima: School of Social Sciences, Waseda University
Manabu Toda: School of Social Sciences, Waseda University

No 2023-1, Working Papers from Waseda University, Faculty of Political Science and Economics

Abstract: We consider two-sided one-to-one matching problems (between men and women) and study a new requirement called “own-side singles monotonicity.” 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 (with the same set of agents), we improve (or leave unchanged) her ranking for each agent on the opposite side of her. Own-side singles monotonicity requires that each agent on her side should not be made better off (except for her). Unfortunately, no single-valued solution satisfies own-side singles monotonicity and stability. However, there is a (multi-valued) solution, the stable solution, that does. We provide two characterizations of the stable solution based on this property. It is the unique solution satisfying weak unanimity, null player invariance, own-side singles monotonicity, and consistency. The uniqueness also holds by replacing consistency with Maskin invariance. In addition, we study the impact of improving her ranking on the welfare of the agents on the opposite side of her.

Keywords: property regimes, one-to-one matching; own-side singles monotonicity; other-side singles monotonicity; stability; consistency; Maskin invariance. (search for similar items in EconPapers)
JEL-codes: C71 C78 D47 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2021-03
New Economics Papers: this item is included in nep-des and nep-mic
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