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Fuzzy Cores and Fuzzy Balancedness

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  • Gulick, G. van
  • Norde, H.W.

    (Tilburg University, Center for Economic Research)

Abstract

We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that any fuzzy game has a non-empty core if and only if it satisfies all (fuzzy) balanced inequalities. We also consider deposit games to illustrate the use of the main result.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2011-062.

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Date of creation: 2011
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Handle: RePEc:dgr:kubcen:2011062

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Web page: http://center.uvt.nl

Related research

Keywords: Cooperative fuzzy games; fuzzy balancedness; fuzzy core;

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  1. Gulick, G. van & Borm, P.E.M. & De Waegenaere, A.M.B. & Hendrickx, R.L.P., 2007. "Deposit Games with Reinvestment," Discussion Paper 2007-22, Tilburg University, Center for Economic Research.
  2. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Discussion Paper 2002-13, Tilburg University, Center for Economic Research.
  3. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
  4. Yan-An Hwang & Yu-Hsien Liao, 2010. "The unit-level-core for multi-choice games: the replicated core for TU games," Journal of Global Optimization, Springer, vol. 47(2), pages 161-171, June.
  5. Yaron Azrieli & Ehud Lehrer, 2007. "Market Games in Large Economies with a Finite Number of Types," Economic Theory, Springer, vol. 31(2), pages 327-342, May.
  6. Tijs, S.H. & Brânzei, R. & Ishihara, S. & Muto, S., 2004. "On cores and stable sets for fuzzy games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142599, Tilburg University.
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