IDEAS home Printed from https://ideas.repec.org/p/dpr/wpaper/0651.html
   My bibliography  Save this paper

Preference Revelation Games and Strong Cores of Allocation Problems with Indivisibilities

Author

Listed:
  • Koji Takamiya

Abstract

This paper studies the incentive compatibility of solutions to generalized indivisible good allocation problems introduced by Sonmez (1999), which contain the well-known marriage problems (Gale and Shapley, 1962) and the housing markets (Shapley and Scarf, 1974) as special cases. In particular, I consider the vulnerability to manipulation of solutions that are individually rational and Pareto optimal. By the results of Sonmez (1999) and Takamiya (2003), any individually rational and Pareto optimal solution is strategy-proof if and only if the strong core correspondence is essentially single-valued, and the solution is a strong core selection. Given this fact, this paper examines the equilibrium outcomes of the preference revelation games when the strong core correspondence is not necessarily essentially single-valued. I show that for the preference revelation games induced by any solution which is individually rational and Pareto optimal, the set of strict strong Nash equilibrium outcomes coincides with the strong core. This generalizes one of the results by Shin and Suh (1996) obtained in the context of the marriage probelms. Further, I examine the other preceding results proved for the marriage problems (Alcalde, 1996; Shin and Suh, 1996; Sonmez, 1997) to find that none of those results are generalized to the general model.

Suggested Citation

  • Koji Takamiya, 2006. "Preference Revelation Games and Strong Cores of Allocation Problems with Indivisibilities," ISER Discussion Paper 0651, Institute of Social and Economic Research, Osaka University.
  • Handle: RePEc:dpr:wpaper:0651
    as

    Download full text from publisher

    File URL: http://www.iser.osaka-u.ac.jp/library/dp/2006/DP0651.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. 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.
    2. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
    3. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, May.
    4. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
    5. 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.
    6. William Thomson, 1984. "The Manipulability of Resource Allocation Mechanisms," Review of Economic Studies, Oxford University Press, vol. 51(3), pages 447-460.
    7. Thomson, William, 1988. "The Manipulability of the Shapley-Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 101-127.
    8. Koji Takamiya, 2003. "On strategy-proofness and essentially single-valued cores: A converse result," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(1), pages 77-83.
    9. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:dpr:wpaper:0651. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Fumiko Matsumoto). General contact details of provider: http://edirc.repec.org/data/isosujp.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.