IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v1y1991i1p108-16.html
   My bibliography  Save this article

On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game

Author

Listed:
  • Shapley, Lloyd
  • Vohra, Rajiv

Abstract

We provide elementary proofs of Scarf's theorem on the non-emptiness of the core and of the K-K-M-S theorem, based.on Kakutani's fixed point theorem. We also show how these proofs can be modified to apply a coincidence theorem of Fan instead of Kakutani's fixed point theorem, for some additional simplicity.

Suggested Citation

  • Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 108-116, January.
    • Handle: RePEc:spr:joecth:v:1:y:1991:i:1:p:108-16
    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. Nizar Allouch & Arkadi Predtetchinski, 2008. "On the non-emptiness of the fuzzy core," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 203-210, June.
    2. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 353-370, January.
    3. Yakar Kannai & Wooders, Myrna H., 1999. "A Further Extension of the KKMS Theorem," The Warwick Economics Research Paper Series (TWERPS) 538, University of Warwick, Department of Economics.
    4. Abe, Takaaki & Funaki, Yukihiko, 2021. "The unbinding core for coalitional form games," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 39-42.
    5. Jean Guillaume Forand & Metin Uyanık, 2019. "Fixed-point approaches to the proof of the Bondareva–Shapley Theorem," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 117-124, May.
    6. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    7. Bialek, William & DeWeese, Michael & Rieke, Fred & Warland, David, 1993. "Bits and brains: Information flow in the nervous system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 581-593.
    8. Jiuqiang Liu & Xiaodong Liu, 2014. "Existence of Edgeworth and competitive equilibria and fuzzy cores in coalition production economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 975-990, November.
    9. Yakar Kannai, 2013. "Using oriented volume to prove Sperner’s lemma," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 11-19, May.
    10. Nicolò, Antonio & Salmaso, Pietro & Sen, Arunava & Yadav, Sonal, 2023. "Stable sharing," Games and Economic Behavior, Elsevier, vol. 141(C), pages 337-363.
    11. Takaaki Abe & Yukihiko Funaki, 2018. "The Unbinding Core for Coalitional Form Games," Working Papers 1805, Waseda University, Faculty of Political Science and Economics.
    12. Liu, Jiuqiang & Tian, Hai-Yan, 2014. "Existence of fuzzy cores and generalizations of the K–K–M–S theorem," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 148-152.
    13. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    14. P. J. J. Herings & A. J. J. Talman, 1998. "Intersection Theorems with a Continuum of Intersection Points," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 311-335, February.
    15. Azrieli, Yaron & Shmaya, Eran, 2014. "Rental harmony with roommates," Journal of Economic Theory, Elsevier, vol. 153(C), pages 128-137.
    16. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    17. Liu, Jiuqiang & Liu, Xiaodong, 2013. "A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 150-156.

    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:1:y:1991:i:1:p:108-16. 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.