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Epsilon cores of games and economies with limited side payments

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  • Alexander Kovalenkovy
  • Wooders, Myrna Holtz

Abstract

We introduce the concept of a parameterized collection of games with limited side payments, ruling out large transfers of utility. Under the assumption that the payoff set of the grand coalition is convex, we show that a game with limited side payments has a nonempty E-core. Our main result is that, when some degree of side-paymentness within nearly-effective small groups is assumed, then all payoffs in the E-core treat similar players similarly. A bound on the distance between E-core payoffs of any two similar players is given in terms of the parameters describing the game. These results add to the literature showing that games with many players and small effective groups have the properties of competitive markets.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp536.pdf
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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 536.

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Length: 23 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:wrk:warwec:536

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Keywords: cooperative games ; equal treatment ; core convergence ; 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. 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.
  2. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, Springer, vol. 20(4), pages 419-27.
  3. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, Econometric Society, vol. 59(1), pages 123-38, January.
  4. Mamoru Kaneko, 1980. "The Central Assignment Game and the Assignment Markets," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 563, Cowles Foundation for Research in Economics, Yale University.
  5. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 657, Cowles Foundation for Research in Economics, Yale University.
  6. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, Elsevier, vol. 1(1), pages 9-25, June.
  7. 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.
  8. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, Econometric Society, vol. 62(5), pages 1141-60, September.
  9. Kovalenkov, Alexander & Wooders, Myrna, 2003. "Approximate cores of games and economies with clubs," Journal of Economic Theory, Elsevier, Elsevier, vol. 110(1), pages 87-120, May.
  10. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, Elsevier, vol. 3(4), pages 313-327, December.
  11. 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.
  12. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 64, pages 416.
  13. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1483-87, November.
  14. 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.
  15. 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.
  16. Garratt, Rod & Qin, Cheng-Zhong, 1997. "On a Market for Coalitions with Indivisible Agents and Lotteries," Journal of Economic Theory, Elsevier, Elsevier, vol. 77(1), pages 81-101, November.
  17. Myrna Holtz Wooders, 1996. "Equivalence of Lindahl equilibrium with participation prices and the core (*)," Economic Theory, Springer, Springer, vol. 9(1), pages 115-127.
  18. Mas-Colell, Andreu, 1979. "A refinement of the core equivalence theorem," Economics Letters, Elsevier, Elsevier, vol. 3(4), pages 307-310.
  19. Kovalenkov, A. & Wooders, M.H., 1997. "Three Theorems on Non-Emptiness of Approximate Cores: Part 2. Economies with Clubs," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 391.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  20. Wooders, Myrna Holtz & Zame, William R., 1987. "Large games: Fair and stable outcomes," Journal of Economic Theory, Elsevier, Elsevier, vol. 42(1), pages 59-93, June.
  21. Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, Elsevier, vol. 55(2), pages 400-415, December.
  22. Scotchmer, S. & Wooders, M.H., 1988. "Monotonicity in games that Exhaust Gains to Scale," Papers, Stanford - Institute for Thoretical Economics 525, Stanford - Institute for Thoretical Economics.
  23. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on," Working Papers mwooders-98-04, University of Toronto, Department of Economics.
  24. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1327-50, November.
  25. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  26. Mas-Colell, Andreu, 1975. "A further result on the representation of games by markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(1), pages 117-122, February.
  27. 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.
  28. Kovalenkov, A. & Wooders, M.H., 1997. "Three Theorems on Non-Emptiness of Approximate Cores: Part 1. Game Theoretic Results," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 390.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  29. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, Econometric Society, vol. 38(6), pages 791-815, November.
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Cited by:
  1. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on e for non-emptiness of the e-core of an arbitrary game with side payments," Working Papers mwooders-98-05, University of Toronto, Department of Economics.
  2. Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "Approximate Cores Of Games And Economies With Clubs," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 535, University of Warwick, Department of Economics.
  3. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on," Working Papers mwooders-98-04, University of Toronto, Department of Economics.
  4. 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), University of Warwick, Department of Economics 641, University of Warwick, Department of Economics.

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