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

Author

Listed:
  • Yoichi Kasajima

    (School of Social Sciences, Waseda University)

  • Manabu Toda

    (School of Social Sciences, Waseda University)

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.

Suggested Citation

  • Yoichi Kasajima & Manabu Toda, 2021. "Singles monotonicity and stability in one-to-one matching problems," Working Papers 2023-1, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:2023-1
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    References listed on IDEAS

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    More about this item

    Keywords

    property regimes; 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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