Fuzzy cores and fuzzy balancedness

We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (Problemy Kibernet 10:119–139, <CitationRef CitationID="CR4">1963</CitationRef>) and Shapley (Naval Res Logist Q 14: 453–460, <CitationRef CitationID="CR11">1967</CitationRef>). 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 is balanced. We also consider deposit games to illustrate the use of the main result. Copyright Springer-Verlag Berlin Heidelberg 2013