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

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  • Kasajima, Yoichi
  • Toda, Manabu

Abstract

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.

Suggested Citation

  • Kasajima, Yoichi & Toda, Manabu, 2024. "Singles monotonicity and stability in one-to-one matching problems," Games and Economic Behavior, Elsevier, vol. 143(C), pages 269-286.
    • Handle: RePEc:eee:gamebe:v:143:y:2024:i:c:p:269-286
    DOI: 10.1016/j.geb.2023.11.001
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    1. Qiufu Chen & Yuanmei Li & Xiaopeng Yin & Luosai Zhang & Siyi Zhou, 2024. "The Machiavellian frontier of stable mechanisms," Papers 2405.12804, arXiv.org, revised Jul 2024.

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    More about this item

    Keywords

    One-to-one matching; Own-side singles monotonicity; Other-side singles monotonicity; Stability; Consistency; Maskin invariance;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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