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

Author

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  • 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
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    References listed on IDEAS

    as
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    6. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
    7. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    8. 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.
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    10. Kannai, Yakar, 1992. "The core and balancedness," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 12, pages 355-395, Elsevier.
    11. 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)

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    More about this item

    Keywords

    Market games; cooperative games; large games; club economies; local public goods; differentiated commodities; abstract economies;
    All these keywords.

    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

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