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A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core

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  • Liu, Jiuqiang
  • Liu, Xiaodong

Abstract

In 2004, Predtetchinski and Herings [A. Predtetchinski, P.J.J. Herings, “A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game”, Journal of Economic Theory 116 (2004) 84–92] provided a necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game. In this paper, we extend this theorem to its counterpart in fuzzy games and give a necessary and sufficient condition for a non-transferable utility fuzzy game to have a non-empty fuzzy core. As a consequence, we derive a necessary and sufficient condition for non-emptiness of the fuzzy core of a TU fuzzy game.

Suggested Citation

  • Liu, Jiuqiang & Liu, Xiaodong, 2013. "A necessary and sufficient condition for an NTU fuzzy game to have a non-empty fuzzy core," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 150-156.
    • Handle: RePEc:eee:mateco:v:49:y:2013:i:2:p:150-156
    DOI: 10.1016/j.jmateco.2012.12.002
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    References listed on IDEAS

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    1. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    2. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    3. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, February.
    4. Zhou, Lin, 1994. "A Theorem on Open Coverings of a Simplex and Scarf's Core Existence Theorem through Brouwer's Fixed Point Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 473-477, May.
    5. Nizar Allouch & Arkadi Predtetchinski, 2008. "On the non-emptiness of the fuzzy core," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 203-210, June.
    6. Yaron Azrieli & Ehud Lehrer, 2007. "On some families of cooperative fuzzy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 1-15, September.
    7. Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 108-116, January.
    8. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    9. Jean-Pierre Aubin, 1981. "Cooperative Fuzzy Games," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 1-13, February.
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    Cited by:

    1. Liu, Jiuqiang & Tian, Hai-Yan, 2014. "Existence of fuzzy cores and generalizations of the K–K–M–S theorem," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 148-152.
    2. Jiuqiang Liu & Xiaodong Liu, 2014. "Existence of Edgeworth and competitive equilibria and fuzzy cores in coalition production economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 975-990, November.
    3. Qi-Qing Song & Min Guo, 2022. "On Existence of alpha-Core Solutions for Games with Finite or Infinite Players," Papers 2211.03112, arXiv.org, revised Jan 2023.

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