Core and Superdifferential of a Fuzzy $$TU$$-Cooperative Game
V. A. Vasilʹev · Automation and Remote Control · 2021
In the paper, we consider conditions providing the coincidence of the cores and superdifferentials of fuzzy cooperative games with side payments. It turned out that weak homogeneity is one of the simplest sufficient conditions. Moreover, by applying the 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 the subdifferential calculus, we describe a structure of the core for classical fuzzy extensions of the ordinary cooperative game (e.g., the Aubin and Owen extensions) as well as for some new continuations, like the generalized Airport game.