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Approximate cores of games and economies with clubs

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  • Alexander Kovalenkov
  • Myrna H. Wooders

Abstract

We introduce the framework of parameterized collections of games and provide three nonemptiness of approximate core theorems for arbitrary games with and without sidepayments. The parameters bound (a) the number of approx-imate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. The theorems are based on a new notion of partition-balanced pro les and approximately partition-balanced profiles. The results are then applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number mwooders-00-01.

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Length: 33 pages
Date of creation: 11 Nov 1998
Date of revision:
Handle: RePEc:tor:tecipa:mwooders-00-01

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Keywords: cooperative games; clubs; local public goods; games without side payments (NTU games); large games; approximate cores; effective small groups; parameterized collections of games.;

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References

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  1. Alexander Kovalenkovy & Wooders, Myrna Holtz, 1999. "Epsilon cores of games and economies with limited side payments," The Warwick Economics Research Paper Series (TWERPS) 536, University of Warwick, Department of Economics.
  2. 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.
  3. Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "An Explicit Bound on E For Nonemptimess of E-Cores of Games," The Warwick Economics Research Paper Series (TWERPS) 537, University of Warwick, Department of Economics.
  4. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," 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 16, pages 485-541 Elsevier.
  5. 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.
  6. Myrna Holtz Wooders, 1992. "Large Games and Economies With Effective Small Groups," Discussion Paper Serie B 215, University of Bonn, Germany, revised Aug 1992.
  7. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
  8. Hans Wiesmeth & Valery Vasil'ev & Shlomo Weber, 1995. "Core equivalence with congested public goods," Economic Theory, Springer, vol. 6(3), pages 373-387.
  9. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  10. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
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  12. Nir Dagan & Roberto Serrano & Oscar Volij, 1996. "Bargaining, coalitions and competition," Economics Working Papers 178, Department of Economics and Business, Universitat Pompeu Fabra.
  13. Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies," Journal of Economic Theory, Elsevier, vol. 49(1), pages 135-168, October.
  14. Conley, John P. & Wooders, Myrna H., 2001. "Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics," Journal of Economic Theory, Elsevier, vol. 98(2), pages 261-294, June.
  15. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation for Research in Economics, Yale University.
  16. Conley John P., 1994. "Convergence Theorems on the Core of a Public Goods Economy: Sufficient Conditions," Journal of Economic Theory, Elsevier, vol. 62(1), pages 161-185, February.
  17. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
  18. Mas-Colell, Andreu, 1979. "A refinement of the core equivalence theorem," Economics Letters, Elsevier, vol. 3(4), pages 307-310.
  19. 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.
  20. F. Forges & A. Heifetz & E. Minelli, 1999. "Incentive compatible core and competitive equilibria in differential information economies," THEMA Working Papers 99-06, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  21. Ostroy, Joseph M, 1984. "A Reformulation of the Marginal Productivity Theory of Distribution," Econometrica, Econometric Society, vol. 52(3), pages 599-630, May.
  22. Kaneko, Mamoru & Wooders, Myrna Holtz, 1986. "The core of a game with a continuum of players and finite coalitions: The model and some results," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 105-137, October.
  23. Shubik, Martin & Wooders, Myrna Holtz, 1983. "Approximate cores of replica games and economies. Part I: Replica games, externalities, and approximate cores," Mathematical Social Sciences, Elsevier, vol. 6(1), pages 27-48, October.
  24. Shubik, Martin, 1971. "The "Bridge Game" Economy: An Example of Indivisibilities," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 909-12, July-Aug..
  25. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
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  27. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November.
  28. Myrna Holtz Wooders, 1981. "The Epsilon Core of a Large Game," Cowles Foundation Discussion Papers 612, Cowles Foundation for Research in Economics, Yale University.
  29. Conley, John P. & Wooders, Myrna H., 1997. "Equivalence of the Core and Competitive Equilibrium in a Tiebout Economy with Crowding Types," Journal of Urban Economics, Elsevier, vol. 41(3), pages 421-440, May.
  30. Wooders, Myrna, 1978. "Equilibria, the core, and jurisdiction structures in economies with a local public good," Journal of Economic Theory, Elsevier, vol. 18(2), pages 328-348, August.
  31. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer, vol. 25(2), pages 245-58.
  32. Hammond, Peter J., 1999. "On f-core equivalence with general widespread externalities," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 177-184, October.
  33. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-38, January.
  34. Bennett, Elaine & Wooders, Myrna, 1979. "Income distribution and firm formation," Journal of Comparative Economics, Elsevier, vol. 3(3), pages 304-317, September.
  35. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  36. Julian Manning, 1994. "Efficiency in Economies with Jurisdictions and Public Projects," Public Economics 9406004, EconWPA.
  37. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1998. "Equilibrium in a Finite Local Public Goods Economy," Journal of Economic Theory, Elsevier, vol. 79(2), pages 224-244, April.
  38. Hammond, Peter J. & Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "Continuum economies with finite coalitions: Core, equilibria, and widespread externalities," Journal of Economic Theory, Elsevier, vol. 49(1), pages 113-134, October.
  39. Garratt, Rod & Qin, Cheng-Zhong, 1996. "Cores and Competitive Equilibria with Indivisibilities and Lotteries," Journal of Economic Theory, Elsevier, vol. 68(2), pages 531-543, February.
  40. Gerard Debreu, 1961. "New Concepts and Techniques for Equilibrium Analysis," Cowles Foundation Discussion Papers 129, Cowles Foundation for Research in Economics, Yale University.
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  43. Mas-Colell, Andreu, 1980. "Efficiency and Decentralization in the Pure Theory of Public Goods," The Quarterly Journal of Economics, MIT Press, vol. 94(4), pages 625-41, June.
  44. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on," Working Papers mwooders-98-04, University of Toronto, Department of Economics.
  45. Conley, John P. & Wooders, Myrna, 1996. "Taste-homogeneity of optimal jurisdictions in a Tiebout economy with crowding types and endogenous educational investment choices," Ricerche Economiche, Elsevier, vol. 50(4), pages 367-387, December.
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