On the Equivalence of G-weak and -strong Cores in the Marriage Problem
In the marriage problem (two-sided one-to-one matching problem), it is well-known that the weak core, the strong core and the set of stable matchings are all equivalent. This paper generalizes the above observation considering the G-weak core and the G-strong core. These are core concepts in which blocking power is restricted to the coalitions belonging to the prescribed class of coalitions G. I give a necessary and sufficient condition that G should satisfy for the equivalence of the G-weak core and the G-strong core.
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|Date of revision:||Jul 2006|
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- Ma Jinpeng, 1995. "Stable Matchings and Rematching-Proof Equilibria in a Two-Sided Matching Market," Journal of Economic Theory, Elsevier, vol. 66(2), pages 352-369, August.
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- Ehud Kalai, 1978. "A Group Incentive Compatible Mechanism Yielding Core Allocation," Discussion Papers 329, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Shin, Sungwhee & Suh, Sang-Chul, 1996. "A mechanism implementing the stable rule in marriage problems," Economics Letters, Elsevier, vol. 51(2), pages 185-189, May.
- Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
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