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Partnership-enhancement and stability in matching problems

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  • Koichi Tadenuma

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Abstract

In two-sided matching problems, we consider “natural” changes in preferences 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 becomes 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. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Koichi Tadenuma, 2013. "Partnership-enhancement and stability in matching problems," Review of Economic Design, Springer;Society for Economic Design, vol. 17(2), pages 151-164, June.
  • Handle: RePEc:spr:reecde:v:17:y:2013:i:2:p:151-164
    DOI: 10.1007/s10058-012-0137-3
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    File URL: http://hdl.handle.net/10.1007/s10058-012-0137-3
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    References listed on IDEAS

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    1. Hervé Moulin, 1987. "The Pure Compensation Problem: Egalitarianism Versus Laissez-Fairism," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 769-783.
    2. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    3. Thomson, William, 1993. "The replacement principle in public good economies with single-peaked preferences," Economics Letters, Elsevier, vol. 42(1), pages 31-36.
    4. Sprumont, Yves, 1996. "Axiomatizing Ordinal Welfare Egalitarianism When Preferences May Vary," Journal of Economic Theory, Elsevier, vol. 68(1), pages 77-110, January.
    5. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    6. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February.
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    More about this item

    Keywords

    Two-sided matching problem; Stable matching; Partnership; Solidarity; Minimal envy; C78; C71; D71; D63;

    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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