Partnership-Enhancement and Stability in Matching Problems
AbstractIn 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 rankenhancements 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.
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Bibliographic InfoPaper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2010-04.
Length: 23 p.
Date of creation: Apr 2010
Date of revision:
two-sided matching problem; stable matching; partnership; solidarity;
Other versions of this item:
- Koichi Tadenuma, 2013. "Partnership-enhancement and stability in matching problems," Review of Economic Design, Springer, vol. 17(2), pages 151-164, June.
- Tadenuma, Koichi, 2010. "Partnership-Enhancement and Stability in Matching Problems," CCES Discussion Paper Series 30, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
- Koichi Tadenuma, 2010. "Partnership-Enhancement and Stability in Matching Problems," Global COE Hi-Stat Discussion Paper Series gd10-137, Institute of Economic Research, Hitotsubashi University.
- 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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- Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February.
- Moulin, Herve, 1987. "The Pure Compensation Problem: Egalitarianism versus Laissez-Fairism," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 769-83, November.
- Sprumont, Yves, 1996. "Axiomatizing Ordinal Welfare Egalitarianism When Preferences May Vary," Journal of Economic Theory, Elsevier, vol. 68(1), pages 77-110, January.
- Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
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