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Advances In The Theory Of Large Cooperative Games And Applications To Club Theory : The Side Payments Case

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  • Kovalenkov, Alexander

    (University of North Carolina at Chapel Hill)

  • Wooders, Myrna

    (University of Warwick)

Abstract

In a series of papers (Kovalenkov and Wooders 2001a, Games and Economic Behavior, 2001b,Mathematics of Operations Research, and 1997, Journal of Economic Theory to appear), the authors have developed the framework of parameterized collections of games and also that of parameterized collections of economies with clubs. These papers apply to collections of games with nontransferable utility and similarly to economies with clubs and general preferences. The game theoretic framework encompasses the earlier `pregame' framework (cf., Wooders 1994b Econometrica) and also earlier models of economies with clubs and with possibly multiple memberships in clubs (cf. Shubik and Wooders 1982). In this paper, we consider the special case of games with side payments and illustrate the application of our more general results in this special, and much simpler but still important, framework. The motivation for this line of research is developed and application to environmental problems is discussed.

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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 641.

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Length: 28 pages
Date of creation: 2002
Date of revision:
Handle: RePEc:wrk:warwec:641

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Keywords: cooperative games ; clubs ; core ; approximate cores ; widespread externalities ; multiple memberships ; local public goods;

References

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  1. Le Breton, M. & Owen, G. & Weber, S., 1991. "Strongly Balanced Cooperative Games," G.R.E.Q.A.M., Universite Aix-Marseille III 91a09, Universite Aix-Marseille III.
  2. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 26(2), pages 286-336, January.
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  4. Kovalenkov, Alexander & Wooders, Myrna Holtz, 2002. "Approximate Cores Of Games And Economies With Clubs," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 634, University of Warwick, Department of Economics.
  5. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 182R, Cowles Foundation for Research in Economics, Yale University.
  6. Hammond, Peter J. & Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "Continuum economies with finite coalitions: Core, equilibria, and widespread externalities," Journal of Economic Theory, Elsevier, Elsevier, vol. 49(1), pages 113-134, October.
  7. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, Econometric Society, vol. 38(6), pages 791-815, November.
  8. Kovalenkov, A. & Holtz Wooders, M., 1997. "Epsilon Cores of Games and Economies With Limited Side Payments," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 392.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. Forges, Françoise & Heifetz, Aviad & Minelli, Enrico, 2001. "Incentive compatible core and competitive equilibria in differential information economies," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/5451, Paris Dauphine University.
  10. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer, Springer, vol. 25(2), pages 245-58.
  11. 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.
  12. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  13. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1327-50, November.
  14. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 92(6), pages 991-1016, December.
  15. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R Zame, 2003. "Clubs and the Market," Levine's Working Paper Archive 618897000000000754, David K. Levine.
  16. Hammond, Peter J., 1999. "On f-core equivalence with general widespread externalities," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 177-184, October.
  17. Wooders, Myrna, 1978. "Equilibria, the core, and jurisdiction structures in economies with a local public good," Journal of Economic Theory, Elsevier, Elsevier, vol. 18(2), pages 328-348, August.
  18. Alexander Kovalenkov & Myrna H. Wooders, 1999. "An explicit bound on epsilon for nonemptiness of Epsilon-cores of games," Working Papers mwooders-00-03, University of Toronto, Department of Economics.
  19. Mas-Colell, Andreu, 1979. "A refinement of the core equivalence theorem," Economics Letters, Elsevier, Elsevier, vol. 3(4), pages 307-310.
  20. 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, Elsevier, vol. 49(1), pages 135-168, October.
  21. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, Elsevier, vol. 3(4), pages 389-396, December.
  22. 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, Elsevier, vol. 6(1), pages 27-48, October.
  23. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 620, Cowles Foundation for Research in Economics, Yale University.
  24. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1483-87, November.
  25. Yi, Sang-Seung, 1997. "Stable Coalition Structures with Externalities," Games and Economic Behavior, Elsevier, Elsevier, vol. 20(2), pages 201-237, August.
  26. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, Elsevier, vol. 14(1), pages 90-123, May.
  27. Myrna Holtz Wooders, 1992. "Large Games and Economies With Effective Small Groups," Discussion Paper Serie B, University of Bonn, Germany 215, University of Bonn, Germany, revised Aug 1992.
  28. Wooders, Myrna Holtz, 1992. "Inessentiality of Large Groups and the Approximate Core Property: An Equivalence Theorem," Economic Theory, Springer, Springer, vol. 2(1), pages 129-47, January.
  29. Allouch, Nizar & Wooders, Myrna, 2002. "Competitive Pricing In Socially Networked Economies," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 639, University of Warwick, Department of Economics.
  30. Bennett, Elaine & Wooders, Myrna, 1979. "Income distribution and firm formation," Journal of Comparative Economics, Elsevier, vol. 3(3), pages 304-317, September.
  31. Kannai, Yakar, 1992. "The core and balancedness," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 12, pages 355-395 Elsevier.
  32. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
  33. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, Econometric Society, vol. 62(5), pages 1141-60, September.
  34. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, Elsevier, vol. 1(1), pages 9-25, June.
  35. Demange, G., 1991. "Intermediate Preferences and Stable Coalition Structures," DELTA Working Papers, DELTA (Ecole normale supérieure) 91-16, DELTA (Ecole normale supérieure).
  36. Ostroy, Joseph M, 1984. "A Reformulation of the Marginal Productivity Theory of Distribution," Econometrica, Econometric Society, Econometric Society, vol. 52(3), pages 599-630, May.
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  38. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, Econometric Society, vol. 49(2), pages 437-50, March.
  39. Conley, John P. & Wooders, Myrna H., 2001. "Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics," Journal of Economic Theory, Elsevier, Elsevier, vol. 98(2), pages 261-294, June.
  40. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457 Elsevier.
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  42. 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, Elsevier, vol. 12(2), pages 105-137, October.
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