Fuzzy Cores and Fuzzy Balancedness

G. van Gulick, H.W. Norde

Research output: Working paperDiscussion paperOther research output

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Volume2011-062
Publication statusPublished - 2011

Publication series

NameCentER Discussion Paper
Volume2011-062

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Deposits

Keywords

  • Cooperative fuzzy games
  • fuzzy balancedness
  • fuzzy core

Cite this

van Gulick, G., & Norde, H. W. (2011). Fuzzy Cores and Fuzzy Balancedness. (CentER Discussion Paper; Vol. 2011-062). Tilburg: Econometrics.
van Gulick, G. ; Norde, H.W. / Fuzzy Cores and Fuzzy Balancedness. Tilburg : Econometrics, 2011. (CentER Discussion Paper).
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van Gulick, G & Norde, HW 2011 'Fuzzy Cores and Fuzzy Balancedness' CentER Discussion Paper, vol. 2011-062, Econometrics, Tilburg.

Fuzzy Cores and Fuzzy Balancedness. / van Gulick, G.; Norde, H.W.

Tilburg : Econometrics, 2011. (CentER Discussion Paper; Vol. 2011-062).

Research output: Working paperDiscussion paperOther research output

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N2 - 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.

AB - 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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van Gulick G, Norde HW. Fuzzy Cores and Fuzzy Balancedness. Tilburg: Econometrics. 2011. (CentER Discussion Paper).