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On the equivalence of G-weak and -strong cores in the marriage problem

Author

Listed:
  • Koji Takamiya

    (Institute of Social and Economic Research)

Abstract

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.

Suggested Citation

  • Koji Takamiya, 2006. "On the equivalence of G-weak and -strong cores in the marriage problem," Economics Bulletin, AccessEcon, vol. 3(20), pages 1-8.
    • Handle: RePEc:ebl:ecbull:eb-06c70009
    as

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    References listed on IDEAS

    as
    1. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
    2. Kalai, Ehud & Postlewaite, Andrew & Roberts, John, 1979. "A group incentive compatible mechanism yielding core allocations," Journal of Economic Theory, Elsevier, vol. 20(1), pages 13-22, February.
    3. Sonmez, Tayfun, 1997. "Games of Manipulation in Marriage Problems," Games and Economic Behavior, Elsevier, vol. 20(2), pages 169-176, August.
    4. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
    5. 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.
    6. 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.
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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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