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Approximate Cores of Games and Economies with Clubs

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Author Info
Alexander Kovalenkov (University of North Carolina)
Myrna Holtz Wooders (University of Toronto and University of Warwick)

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Abstract

This presentation focuses on new approachs to large games introduced in five papers by the authors (one with the same title as this abstract). In a new framework of parameterised collections of games with and without side payments, we provide nonemptiness of approximate core, a law of scarcity, and convergence results. The parameters bound (a) the number of approximate 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. Our nonemptiness theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. Our convergence results provide a new sort of application of standard theorems from linear programming. The results are applied to a model of an economy with clubs. In contrast to the extant literature, our approach allows widespread externalities -- that is, the payoffs to members of a club may depend on the economy in which the club is situated.

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1790.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1790

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Myrna Holtz Wooders, 1992. "Large Games and Economies With Effective Small Groups," Discussion Paper Serie B 215, University of Bonn, Germany, revised Aug 1992.
  2. 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. [Downloadable!] (restricted)
  3. Myrna Holtz Wooders, 1981. "The Epsilon Core of a Large Game," Cowles Foundation Discussion Papers 612, Cowles Foundation, Yale University. [Downloadable!]
  4. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation, Yale University. [Downloadable!]
  7. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers 620, Cowles Foundation, Yale University. [Downloadable!]
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  8. Nir Dagan & Roberto Serrano & Oscar Volij, 1996. "Bargaining, Coalitions and Competition," Economics Working Papers 178, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  9. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June. [Downloadable!] (restricted)
  10. 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.
  11. Vasil'ev, Valery & Weber, Shlomo & Wiesmeth, Hans, 1995. "Core Equivalence with Congested Public Goods," Economic Theory, Springer, vol. 6(3), pages 373-87, November.
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  12. Gerard Debreu, 1961. "New Concepts and Techniques for Equilibrium Analysis," Cowles Foundation Discussion Papers 129, Cowles Foundation, Yale University. [Downloadable!]
  13. 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.
  14. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. 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. [Downloadable!] (restricted)
  17. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation, Yale University. [Downloadable!]
  18. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September. [Downloadable!] (restricted)
  19. A. Kovalenkov & M. Holtz Wooders, 1999. "An explicit bound on e for nonemptiness of e-cores of games," THEMA Working Papers 99-37, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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  20. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "Epsilon cores of games and economies with limited side payments," Working Papers mwooders-98-03, University of Toronto, Department of Economics. [Downloadable!]
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  21. Kirman, Alan, 2007. "Introduction," Macroeconomic Dynamics, Cambridge University Press, vol. 11(S1), pages 1-7, November. [Downloadable!]
  22. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November. [Downloadable!] (restricted)
  23. Bennett, Elaine & Wooders, Myrna, 1979. "Income distribution and firm formation," Journal of Comparative Economics, Elsevier, vol. 3(3), pages 304-317, September. [Downloadable!] (restricted)
  24. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July. [Downloadable!] (restricted)
  25. 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. [Downloadable!] (restricted)
  26. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-38, January. [Downloadable!] (restricted)
  27. 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. [Downloadable!] (restricted)
  28. Broome, John, 1972. "Approximate equilibrium in economies with indivisible commodities," Journal of Economic Theory, Elsevier, vol. 5(2), pages 224-249, October. [Downloadable!] (restricted)
  29. 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. [Downloadable!] (restricted)
  30. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on," Working Papers mwooders-98-04, University of Toronto, Department of Economics. [Downloadable!]
  31. Ostroy, Joseph M, 1984. "A Reformulation of the Marginal Productivity Theory of Distribution," Econometrica, Econometric Society, vol. 52(3), pages 599-630, May. [Downloadable!] (restricted)
  32. 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. [Downloadable!] (restricted)
  33. 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. [Downloadable!] (restricted)
  34. Hammond, Peter J., 1999. "On f-core equivalence with general widespread externalities," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 177-184, October. [Downloadable!] (restricted)
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  35. Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, vol. 55(2), pages 400-415, December. [Downloadable!] (restricted)
  36. Forges, F. & Heifetz, A. & Minelli, E., 1999. "Incentive Compatible Core and Competitive Equilibria in Differential Information Economies," Papers 34-99, Tel Aviv.
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  37. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-50, November. [Downloadable!] (restricted)
  38. 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. [Downloadable!] (restricted)
  39. 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. [Downloadable!] (restricted)
  40. 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.. [Downloadable!] (restricted)
  41. 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. [Downloadable!] (restricted)
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  42. 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. [Downloadable!] (restricted)
  43. Wooders,Myrna, . "The efficaciousness of small groups and the approximate core property in games without side payments: Some first results," Discussion Paper Serie B 179, University of Bonn, Germany.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Edward Cartwright & Myrna Wooders, 2005. "The Law od Demand in Tiebout Economies," Working Papers 0527, Department of Economics, Vanderbilt University. [Downloadable!]
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  2. Tone Arnold & Myrna Wooders, 2005. "Dynamic Club Formation with Coordination," Working Papers 0522, Department of Economics, Vanderbilt University. [Downloadable!]
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  3. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer, vol. 38(1), pages 137-153, March. [Downloadable!] (restricted)
    Other versions:
  4. Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "A law of scarcity for games," The Warwick Economics Research Paper Series (TWERPS) 546, University of Warwick, Department of Economics. [Downloadable!]
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  5. Nizar Allouch & John P. Conley & Myrna Wooders, 2008. "Anonymous Price Taking Equilibrium in Tiebout Economies with a Continuum of Agents; Existence and Characterization," Working Papers 0811, Department of Economics, Vanderbilt University. [Downloadable!]
  6. Edward Cartwright & Myrna Wooders, 2005. "Correlated Equilibrium and Behavioral Conformity," Working Papers 0526, Department of Economics, Vanderbilt University. [Downloadable!]
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  7. 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. [Downloadable!]
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  8. Edward Cartwright & Myrna Wooders, 2003. "Social Conformity and Bounded Rationality in Arbitrary Games with Incomplete Information: Some First Results," Working Papers 2003.119, Fondazione Eni Enrico Mattei. [Downloadable!]
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  9. Nizar Allouch & Myrna Wooders, 2004. "Price taking equilibrium in club economies with multiple memberships and unbounded club sizes," Cahiers de la Maison des Sciences Economiques b04109, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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  10. Kovalenkov, Alexander & Wooders, Myrna, 2002. "Advances In The Theory Of Large Cooperative Games And Applications To Club Theory : The Side Payments Case," The Warwick Economics Research Paper Series (TWERPS) 641, University of Warwick, Department of Economics. [Downloadable!]
  11. Meseguer-Artola, Antoni & Wooders, Myrna Holtz & Martinez-Legaz, Juan-Enrique, 2003. "Representing Games As Coalition Production Economies With Public Goods," The Warwick Economics Research Paper Series (TWERPS) 669, University of Warwick, Department of Economics. [Downloadable!]
  12. Allouch, Nizar & Wooders, Myrna, 2002. "Competitive Pricing In Socially Networked Economies," The Warwick Economics Research Paper Series (TWERPS) 639, University of Warwick, Department of Economics. [Downloadable!]
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