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An explicit bound on e for non-emptiness of the e-core of an arbitrary game with side payments

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  • Alexander Kovalenkov
  • Myrna Holtz Wooders

Abstract

We introduce the concept of a parameterized collection of games with side payments and determine a bound on e so that all sufficiently large games in such a collection have non-empty e -cores. A parameterized collection of games is described by (a) the number of approximate player types and the accuracy of this approximation, (b) the size of approximately effective small groups, and (c) the size of the bound on maximal per capita payoffs achievable in coalitions. An explicit relationship between the required size of e the parameters describing the collection and the number of players in the game under consideration is established. Given the parameters, the larger the number of players in a game, the smaller the e that can be chosen.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number mwooders-98-05.

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Length: 15 pages
Date of creation: 11 Jan 1997
Date of revision:
Handle: RePEc:tor:tecipa:mwooders-98-05

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Related research

Keywords: cooperative games; games with side payments (TU games); approximate cores; effective small groups; parametrized collections of games.;

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References

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  1. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March.
  2. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  3. Scotchmer, S. & Wooders, M.H., 1988. "Monotonicity in games that Exhaust Gains to Scale," Papers 525, Stanford - Institute for Thoretical Economics.
  4. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  5. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November.
  6. 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.
  7. Kovalenkov, A. & Wooders, M.H., 1997. "Three Theorems on Non-Emptiness of Approximate Cores: Part 2. Economies with Clubs," UFAE and IAE Working Papers 391.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  8. 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.
  9. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on," Working Papers mwooders-98-04, University of Toronto, Department of Economics.
  10. Wooders, Myrna Holtz & Zame, William R., 1987. "Large games: Fair and stable outcomes," Journal of Economic Theory, Elsevier, vol. 42(1), pages 59-93, June.
  11. Myrna Holtz Wooders, 1992. "Large Games and Economies With Effective Small Groups," Discussion Paper Serie B 215, University of Bonn, Germany, revised Aug 1992.
  12. Mamoru Kaneko, 1980. "The Central Assignment Game and the Assignment Markets," Cowles Foundation Discussion Papers 563, Cowles Foundation for Research in Economics, Yale University.
  13. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
  14. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  15. Garratt, Rod & Qin, Cheng-Zhong, 1997. "On a Market for Coalitions with Indivisible Agents and Lotteries," Journal of Economic Theory, Elsevier, vol. 77(1), pages 81-101, November.
  16. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
  17. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-50, November.
  18. Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, vol. 55(2), pages 400-415, December.
  19. Weber, S., 1981. "Some results on the weak core of a non-side-payment game with infinitely many players," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 101-111, March.
  20. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-38, January.
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