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The core of a class of non-atomic games which arise in economic applications

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  • Einy, Ezra
  • Moreno, Diego
  • Shitovitz, Benyamin

Abstract

We prove a representation theorem for the core of a non-atomic game of the form v = fOil, where Il is a finite dimensional vector of non-atomic measures and f is a non-decreasing continuous concave function on the range of Il. The theorem is stated in terms of the sub gradients of the function f. As a consequence of this theorem we show that the game v is balanced (i. e., has a non-empty core) iff the function f is homogeneous of degree one along the diagonal of the range of Il, and it is totally balanced (i.e., every subgame of v has a non-empty core) iff the function f is homogeneous of degree one in the entire range of Il. We also apply our results to some non-atomic games which occur in economic applications.

Suggested Citation

  • Einy, Ezra & Moreno, Diego & Shitovitz, Benyamin, 1997. "The core of a class of non-atomic games which arise in economic applications," UC3M Working papers. Economics 6024, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:6024
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    1. Kannai, Yakar, 1992. "The core and balancedness," 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 12, pages 355-395, Elsevier.
    2. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1996. "Core and Stable Sets of Large Games Arising in Economics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 200-211, January.
    3. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
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    Cited by:

    1. M. Amarante & F. Maccheroni & M. Marinacci & L. Montrucchio, 2006. "Cores of non-atomic market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 399-424, October.
    2. Montrucchio, Luigi & Scarsini, Marco, 2007. "Large newsvendor games," Games and Economic Behavior, Elsevier, vol. 58(2), pages 316-337, February.
    3. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2004. "Voluntary formation of communities for the provision of public projects," Journal of Economic Theory, Elsevier, vol. 115(1), pages 1-34, March.
    4. Larry G. Epstein & Massimo Marinacci, 2000. "The Core of Large TU Games," RCER Working Papers 469, University of Rochester - Center for Economic Research (RCER).
    5. Marinacci, Massimo & Montrucchio, Luigi, 2003. "Subcalculus for set functions and cores of TU games," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 1-25, February.
    6. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
    7. Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 923-940, October.
    8. Einy, Ezra & Moreno, Diego & Shitovitz, Benyamin, 1999. "The Asymptotic Nucleolus of Large Monopolistic Market Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 186-206, December.
    9. Epstein, Larry G. & Marinacci, Massimo, 2001. "The Core of Large Differentiable TU Games," Journal of Economic Theory, Elsevier, vol. 100(2), pages 235-273, October.
    10. Einy, Ezra & Moreno, Diego & Shitovitz, Benyamin, 1999. "Fine value allocations in large exchange economies with differential information," UC3M Working papers. Economics 6128, Universidad Carlos III de Madrid. Departamento de Economía.

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