IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Large games and the law of large numbers

  • Al-Najjar, Nabil I.
Registered author(s):

    This paper introduces discrete large games where the set of players is a countable dense 'grid' with a finitely additive distribution. In these games any function from player names to mixed actions is a legitimate strategy profile. No extraneous continuity or measurability conditions are assumed. Randomness can be modeled explicitly and an exact law of large numbers holds. Equilibria enjoy a strong purification property: every realization of every mixed strategy equilibrium is a pure strategy equilibrium almost surely. Every continuum-player game has a discrete large game representation that preserves the original payoffs, strategy profiles and equilibria. It is argued that strategy profiles in continuum-player games have an ambiguous meaning because measurability requirements force the smoothing out of individual variations. These variations have clear strategic meaning in finite-player games and can be expressed in discrete large games, but not when the set of players is the continuum.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.sciencedirect.com/science/article/B6WFW-4RM7N07-1/2/73c6a8957f557a6b3779c479f8cd4093
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 64 (2008)
    Issue (Month): 1 (September)
    Pages: 1-34

    as
    in new window

    Handle: RePEc:eee:gamebe:v:64:y:2008:i:1:p:1-34
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Harald Uhlig, 2010. "A Law of Large Numbers for Large Economies," Levine's Working Paper Archive 2070, David K. Levine.
    2. Al-Najjar, Nabil Ibraheem, 1995. "Decomposition and Characterization of Risk with a Continuum of Random Variables," Econometrica, Econometric Society, vol. 63(5), pages 1195-1224, September.
    3. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    4. Nabil I. Al-Najjar & Luca Anderlini & Leonardo Felli, 2003. "Undescribable Events," CESifo Working Paper Series 1092, CESifo Group Munich.
    5. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    6. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
    8. Al-Najjar, Nabil I., 2004. "Aggregation and the law of large numbers in large economies," Games and Economic Behavior, Elsevier, vol. 47(1), pages 1-35, April.
    9. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
    10. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    11. Dubey, Pradeep & Shapley, Lloyd S., 1994. "Noncooperative general exchange with a continuum of traders: Two models," Journal of Mathematical Economics, Elsevier, vol. 23(3), pages 253-293, May.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:64:y:2008:i:1:p:1-34. 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: (Zhang, Lei)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.