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

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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.

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File URL: http://www.accessecon.com/pubs/VUECON/vu08-w13.pdf
File Function: First version, 2008
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Bibliographic Info

Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0813.

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Date of creation: Aug 2008
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Handle: RePEc:van:wpaper:0813

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

Related research

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

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  1. Evstigneev, I.V. & Flam, S.D., 2000. "Sharing Nonconvex Costs," Norway; Department of Economics, University of Bergen, Department of Economics, University of Bergen 1300, Department of Economics, University of Bergen.
  2. Yaron Azrieli & Ehud Lehrer, 2007. "Market Games in Large Economies with a Finite Number of Types," Economic Theory, Springer, Springer, vol. 31(2), pages 327-342, May.
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