The core and superdifferential of a fuzzy TU-cooperative game

In the paper, we consider conditions providing coincidence of the cores and superdifferentials of fuzzy cooperative games with side payments. It turned out that one of the most simple sufficient conditions consists of weak homogeneity. Moreover, by applying so-called $S^*$-representation of a fuzzy game introduced by the author, we show that for any $v$ with nonempty core $C(v)$ there exists some game $u$ such that $C(v)$ coincides with the superdifferential of $u.$ By applying subdifferential calculus we describe a structure of the core for both classic fuzzy extensions of the ordinary cooperative game (e.g., Aubin and Owen extensions) and for some new continuations, like Harsanyi extensions and generalized Airport game.