Open AccessThe core and superdifferential of a fuzzy TU-cooperative game
Author(s) -
В. А. Васильев,
В. А. Васильев
Publication year - 2020
Publication title -
matematičeskaâ teoriâ igr i eë priloženiâ
Language(s) - English
Resource type - Journals
ISSN - 2074-9872
DOI - 10.17076/mgta_2020_2_14
Subject(s) - core (optical fiber) , fuzzy logic , bondareva–shapley theorem , mathematical economics , mathematics , coincidence , representation (politics) , game theory , algebra over a field , calculus (dental) , computer science , pure mathematics , combinatorial game theory , sequential game , artificial intelligence , law , medicine , telecommunications , alternative medicine , dentistry , pathology , politics , political science
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 vwith 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 forboth 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.