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

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Author Info

  • Diego Moreno

    ()
    (Departmento de Economia, Universidad Carlos III de Madrid, E-28903 Getafe, Spain)

  • Benyamin Shitovitz

    ()
    (Department of Economics, University of Haifa, Mount Carmel, Haifa 31905, Israel)

  • Ezra Einy

    ()
    (Department of Economics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel)

Abstract

We study the core of a non-atomic game v which is uniformly continuous with respect to the DNA-topology and continuous at the grand coalition. Such a game has a unique DNA-continuous extension ${\overline {v}}$ on the space B1 of ideal sets. We show that if the extension ${\overline {v}}$ is concave then the core of the game v is non-empty iff ${\overline {v}}$ is homogeneous of degree one along the diagonal of B1. We use this result to obtain representation theorems for the core of a non-atomic game of the form v=fˆ µ where µ is a finite dimensional vector of measures and f is a concave function. We also apply our results to some non-atomic games which occur in economic applications.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 28 (1999)
Issue (Month): 1 ()
Pages: 1-14

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Handle: RePEc:spr:jogath:v:28:y:1999:i:1:p:1-14

Note: Received May 1998/Revised version September 1998
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Related research

Keywords: Coalitional game · core · non-atomic games;

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Cited by:
  1. 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.
  2. Montrucchio, Luigi & Scarsini, Marco, 2007. "Large newsvendor games," Games and Economic Behavior, Elsevier, vol. 58(2), pages 316-337, February.
  3. Larry G. Epstein & Massimo Marinacci, 2000. "The Core of Large TU Games," RCER Working Papers 469, University of Rochester - Center for Economic Research (RCER).
  4. 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.
  5. 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.
  6. M. Amarante & F. Maccheroni & M. Marinacci & L. Montrucchio, 2006. "Cores of non-atomic market games," International Journal of Game Theory, Springer, vol. 34(3), pages 399-424, October.
  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, vol. 41(4), pages 923-940, October.
  8. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
  9. 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.

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