IDEAS home Printed from https://ideas.repec.org/p/huj/dispap/dp344.html
   My bibliography  Save this paper

Asymptotic Values of Vector Measure Games

Author

Listed:
  • Abraham Neyman

    ()

  • Rann Smorodinsky

    ()

Abstract

The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of ?(S) where ? is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games where a two-house weighted majority game is a game in which a coalition is winning if and only if it is winning in two given weighted majority games. All weighted majority games have an asymptotic value. However, not all two-house weighted majority games have an asymptotic value. In this paper we prove that the existence of infinitely many atoms with sufficient variety suffice for the existence of the asymptotic value in a general class of nonsmooth vector measure games that includes in particular two-house weighted majority games.

Suggested Citation

  • Abraham Neyman & Rann Smorodinsky, 2003. "Asymptotic Values of Vector Measure Games," Discussion Paper Series dp344, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp344
    as

    Download full text from publisher

    File URL: http://ratio.huji.ac.il/sites/default/files/publications/Neyman344.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. R. J. Aumann & M. Kurz & A. Neyman, 1983. "Voting for Public Goods," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 677-693.
    2. Hart, Sergiu, 1977. "Asymptotic value of games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 57-80, March.
    3. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-1161, July.
    4. Neyman, Abraham, 2002. "Values of games with infinitely many players," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 56, pages 2121-2167 Elsevier.
    5. Aumann, R. J. & Kurz, M. & Neyman, A., 1987. "Power and public goods," Journal of Economic Theory, Elsevier, vol. 42(1), pages 108-127, June.
    6. Neyman, Abraham, 2010. "Singular games in bv'NA," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 384-387, July.
    7. A. W. Coats, 1996. "Introduction," History of Political Economy, Duke University Press, vol. 28(5), pages 3-11, Supplemen.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Omer Edhan, 2013. "Values of nondifferentiable vector measure games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 947-972, November.

    More about this item

    Keywords

    asymptotic value; weighted majority game; two-house weighted; majority game; vector measure game; Shapley value;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:huj:dispap:dp344. 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: (Michael Simkin). General contact details of provider: http://edirc.repec.org/data/crihuil.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.