IDEAS home Printed from https://ideas.repec.org/p/van/wpaper/0813.html
   My bibliography  Save this paper

Games with Many Players and Abstract Economies Permitting Differentiated Commodities, Clubs, and Public Goods

Author

Listed:
  • Myrna Wooders

    () (Department of Economics, Vanderbilt University)

Abstract

In a seminal paper relating economic and game theoretic structures, Shapley and Shubik (1969) demonstrate that a game is a market game -- that is, a game derived from a finite-dimensional private goods exchange economy where all participants have continuous, concave utility functions. In this paper, to accommodate models of economies with public goods, clubs, indivisibilities, and other deviations from the classic model of Shapley and Shubik, we demonstrate an equivalence between homogeneous market games with many players, possibly all with different characteristics, and abstract economies permitting differentiated commodities, clubs, public goods, coalition production, unbounded short sales and other deviations from standard economic models. By a homogeneous market game we mean a game derived from a market where all individuals have the same concave and continuous utility function. We also demonstrate that the condition of small group effectiveness -- that small groups of players can realize almost all gains to collective activities -- is equivalent to the condition of asymptotic negligibility -- that small groups of players cannot have significant impacts on average payoff to large groups of players.

Suggested Citation

  • Myrna Wooders, 2008. "Games with Many Players and Abstract Economies Permitting Differentiated Commodities, Clubs, and Public Goods," Vanderbilt University Department of Economics Working Papers 0813, Vanderbilt University Department of Economics.
  • Handle: RePEc:van:wpaper:0813
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/pubs/VUECON/vu08-w13.pdf
    File Function: First version, 2008
    Download Restriction: no

    References listed on IDEAS

    as
    1. Evstigneev, I.V. & Flam, S.D., 2000. "Sharing Nonconvex Costs," Norway; Department of Economics, University of Bergen 1300, Department of Economics, University of Bergen.
    2. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    3. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Some theorems on the existence of competitive equilibrium," Journal of Economic Theory, Elsevier, vol. 11(1), pages 83-93, August.
    4. Wooders, Myrna Holtz, 1992. "Inessentiality of Large Groups and the Approximate Core Property: An Equivalence Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 129-147, January.
    5. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    6. Yaron Azrieli & Ehud Lehrer, 2007. "Market Games in Large Economies with a Finite Number of Types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 327-342, May.
    7. Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, vol. 55(2), pages 400-415, December.
    8. Myrna Holtz Wooders, 1992. "Large Games and Economies With Effective Small Groups," Discussion Paper Serie B 215, University of Bonn, Germany, revised Aug 1992.
    9. Khan, M Ali, 1974. "Some Remarks on the Core of a "Large" Economy," Econometrica, Econometric Society, vol. 42(4), pages 633-642, July.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Market games; cooperative games; large games; club economies; local public goods; differentiated commodities; abstract economies;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:van:wpaper:0813. 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: (John P. Conley). General contact details of provider: http://www.vanderbilt.edu/econ/wparchive/index.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.