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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.

Suggested Citation

  • Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on," Working Papers mwooders-98-04, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:mwooders-98-04
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    References listed on IDEAS

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    1. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 245-258.
    2. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
    3. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
    4. Manelli, Alejandro M, 1991. "Monotonic Preferences and Core Equivalence," Econometrica, Econometric Society, vol. 59(1), pages 123-138, January.
    5. 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.
    6. 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.
    7. Kovalenkov, A. & Holtz Wooders, M., 1997. "Epsilon Cores of Games and Economies With Limited Side Payments," UFAE and IAE Working Papers 392.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    8. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    9. Manelli, Alejandro M., 1991. "Core convergence without monotone preferences and free disposal," Journal of Economic Theory, Elsevier, vol. 55(2), pages 400-415, December.
    10. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
    11. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-1350, November.
    12. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
    13. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    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 390.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
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    Cited by:

    1. Kovalenkov, Alexander & Wooders, Myrna, 2003. "Approximate cores of games and economies with clubs," Journal of Economic Theory, Elsevier, vol. 110(1), pages 87-120, May.
    2. 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.
    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 mwooders-98-05, University of Toronto, Department of Economics.
    4. 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.

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    More about this item

    Keywords

    cooperative games; games without side payments (NTU games); approximate cores; effective small groups; parameterized collections of games;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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