Games with Many Players and Abstract Economies Permitting Differentiated Commodities, Clubs, and Public Goods
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.
|Date of creation:||Aug 2008|
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References listed on IDEAS
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- Alejandro Manelli, 1989.
"Monotonic Preferences and Core Equivalence,"
859, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
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"Some theorems on the existence of competitive equilibrium,"
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Elsevier, vol. 11(1), pages 83-93, August.
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- Wooders, Myrna Holtz, 1992. "Inessentiality of Large Groups and the Approximate Core Property: An Equivalence Theorem," Economic Theory, Springer, vol. 2(1), pages 129-47, January.
- Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, vol. 55(2), pages 400-415, December.
- Khan, M Ali, 1974. "Some Remarks on the Core of a "Large" Economy," Econometrica, Econometric Society, vol. 42(4), pages 633-42, July.
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