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Partnership-Enhancement and Stability in Matching Problems

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  • Tadenuma, Koichi
  • 蓼沼, 宏一

Abstract

In two-sided matching problems, we consider "natural" changes in prefer- ences of agents in which only the rankings of current partners are enhanced. We introduce two desirable properties of matching rules under such rank- enhancements of partners. One property requires that an agent who be- comes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the "irrelevant" agents, whose preferences as well as whose original partners' preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold.
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Suggested Citation

  • Tadenuma, Koichi & 蓼沼, 宏一, 2010. "Partnership-Enhancement and Stability in Matching Problems," Discussion Papers 2010-04, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2010-04
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    References listed on IDEAS

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    Cited by:

    1. 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.

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    More about this item

    Keywords

    two-sided matching problem; stable matching; partnership; solidarity;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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