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An explicit bound on

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  • Alexander Kovalenkov
  • Myrna Holtz Wooders

Abstract

We consider parameterized collections of games without side payments and determine a bound on epsilon so that all sufficiently large games in the collection have non-empty epsilon-cores. The required size of epsilon depends on: (a) the number of approximate player types and the accuracy of this approximation; (b) the size of approximately effective small groups; (c) the size of the bound on maximal per-capita payoffs achievable in coalitions; and (d) a measure on the extent to which the payoff sets of the games are bounded away from being ``flat.'' Our result makes explicit the relationship between the required size of epsilon for non-emptiness of the epsilon-core, the parameters describing the collection.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number mwooders-98-04.

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Length: 25 pages
Date of creation: 11 Feb 1997
Date of revision:
Handle: RePEc:tor:tecipa:mwooders-98-04

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Related research

Keywords: cooperative games; games without side payments (NTU 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. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, Econometric Society, vol. 59(1), pages 123-38, January.
  3. Alexander Kovalenkov & Myrna H. Wooders, 2000. "Epsilon cores of games and economies with limited side payments," Working Papers, University of Toronto, Department of Economics mwooders-00-02, University of Toronto, Department of Economics.
  4. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, Elsevier, vol. 3(4), pages 313-327, December.
  5. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, Econometric Society, vol. 62(5), pages 1141-60, September.
  6. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1483-87, November.
  7. 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.
  8. 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.
  9. 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.
  10. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1327-50, November.
  11. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  12. 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.
  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, Springer, vol. 25(2), pages 245-58.
  14. 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).
  15. 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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Citations

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Cited by:
  1. 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.
  2. Alexander Kovalenkov & Myrna H. Wooders, 2000. "Epsilon cores of games and economies with limited side payments," Working Papers, University of Toronto, Department of Economics mwooders-00-02, University of Toronto, Department of Economics.
  3. 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, University of Toronto, Department of Economics mwooders-98-05, University of Toronto, Department of Economics.
  4. Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "A law of scarcity for games," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 546, University of Warwick, Department of Economics.

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