Geodesic
The core and superdifferential of a fuzzy TU-cooperative game
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 2, pp. 20-35

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: fuzzy cooperative game, $S^*$-representation, superdifferential, the core of a fuzzy game, weak homogeneity. 
@article{MGTA_2020_12_2_a1,
     author = {Valery A. Vasil'ev},
     title = {The core and superdifferential of a fuzzy {TU-cooperative} game},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {20--35},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2020_12_2_a1/}
}
TY  - JOUR
AU  - Valery A. Vasil'ev
TI  - The core and superdifferential of a fuzzy TU-cooperative game
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2020
SP  - 20
EP  - 35
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2020_12_2_a1/
LA  - ru
ID  - MGTA_2020_12_2_a1
ER  - 
%0 Journal Article
%A Valery A. Vasil'ev
%T The core and superdifferential of a fuzzy TU-cooperative game
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2020
%P 20-35
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2020_12_2_a1/
%G ru
%F MGTA_2020_12_2_a1
Valery A. Vasil'ev. The core and superdifferential of a fuzzy TU-cooperative game. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 2, pp. 20-35. http://geodesic.mathdoc.fr/item/MGTA_2020_12_2_a1/