IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v4y1994i3p453-61.html
   My bibliography  Save this article

An Exchange Economy Can Have an Empty Alpha-Core

Author

Listed:
  • Holly, Charles

Abstract

Yannelis has shown that under very mild conditions on preferences, a 2-agent exchange economy has a nonempty x-core. The purpose of the present paper is to demonstrate that an exchange economy with three or more agents can have an empty x-core. Hence, Yannelis' result would not extend to three or more agents. Examples are provided with and without free disposal, and all preferences are described by linear utility functions. These results are compared with those of Scarf, who proved the existence of an x-core solution for a large class of n-person games. The comparison is carried out on two levels. First, since Scarf and Yannelis use different definitions for the x-core of an exchange economy, we compare these definitions. Second, the present results show that a natural extension of Scarf's theorem for n-person games fails if certain feasibility constraints are incorporated.

Suggested Citation

  • Holly, Charles, 1994. "An Exchange Economy Can Have an Empty Alpha-Core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 453-461, May.
    • Handle: RePEc:spr:joecth:v:4:y:1994:i:3:p:453-61
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    2. Martins-da-Rocha, Victor Filipe & Yannelis, Nicholas C., 2011. "Non-emptiness of the alpha-core," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 716, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    3. Yang, Zhe, 2020. "The weak α-core of exchange economies with a continuum of players and pseudo-utilities," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 43-50.
    4. Christian Pietro & Maria Gabriella Graziano & Vincenzo Platino, 2022. "Social loss with respect to the core of an economy with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 487-508, April.
    5. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2023. "Core and stable sets of exchange economies with externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 27-44, April.
    6. Zhao, Jingang, 1996. "The hybrid equilibria and core selection in exchange economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 387-407.
    7. Graziano, Maria Gabriella & Meo, Claudia & Yannelis, Nicholas C., 2017. "Stable sets for exchange economies with interdependent preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 267-286.
    8. Vincenzo Scalzo, 2022. "Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 1-12, May.

    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:spr:joecth:v:4:y:1994:i:3:p:453-61. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.