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Approximate Cores of a General Class of Economies. Part I: Replica Games, Externalities, and Approximate Cores

Sufficient conditions are demonstrated for the non-emptiness of asymptotic cores of sequences of replica games, i.e., for all sufficiently large replications, the games have non-empty approximate cores and the approximation can be made arbitrarily "good." The conditions are simply that the games are superadditive and satisfy a very non-restrictive "per-capita" boundedness assumption (these properties are satisfied by games derived from well-known models of replica economies). It is argued that the results can be applied to a broad class of games derived from economic models, including ones with external economies and diseconomies, indivisibilities and non-convexities. To support this claim, in Part I applications to an economy with local public goods are provided and in Part II, to a general model of a coalition production economy with remarkably few restrictions on production technology sets and with (possibly) indivisibilities in consumption. Additional examples in Part I illustrate the generality of the result.

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File URL: http://cowles.econ.yale.edu/P/cd/d06a/d0618.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 618.

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Length: 36 pages
Date of creation: Feb 1982
Date of revision:
Publication status: Published in Mathematical Social Sciences (1983), 6: 27-48
Handle: RePEc:cwl:cwldpp:618
Note: CFP 591.
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  1. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  2. Martin Shubik, 1969. "The 'Bridge Game' Economy," Cowles Foundation Discussion Papers 267, Cowles Foundation for Research in Economics, Yale University.
  3. Novshek, William & Sonnenschein, Hugo, 1978. "Cournot and Walras equilibrium," Journal of Economic Theory, Elsevier, vol. 19(2), pages 223-266, December.
  4. Wooders, Myrna Holtz, 1988. "Stability of jurisdiction structures in economies with local public goods," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 29-49, February.
  5. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  6. Shapley, Lloyd S & Shubik, Martin, 1969. "On the Core of an Economic System with Externalities," American Economic Review, American Economic Association, vol. 59(4), pages 678-84, Part I Se.
  7. Dreze, J.H. & Greenberg, J., . "Hedonic coalitions: optimality and stability," CORE Discussion Papers RP -403, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Mas-Colell, Andreu, 1980. "Noncooperative approaches to the theory of perfect competition: Presentation," Journal of Economic Theory, Elsevier, vol. 22(2), pages 121-135, April.
  9. Littlechild, Stephen C, 1975. "Common Costs, Fixed Charges, Clubs and Games," Review of Economic Studies, Wiley Blackwell, vol. 42(1), pages 117-24, January.
  10. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-85, September.
  11. Boehm, Volker, 1974. "The Limit of the Core of an Economy with Production," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 143-48, February.
  12. Sondermann, Dieter, 1974. "Economies of scale and equilibria in coalition production economies," Journal of Economic Theory, Elsevier, vol. 8(3), pages 259-291, July.
  13. Milleron, Jean-Claude, 1972. "Theory of value with public goods: A survey article," Journal of Economic Theory, Elsevier, vol. 5(3), pages 419-477, December.
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