Geodesic
An analog of Bondareva--Shapley theorem~II. Examples of $V$-balanced fuzzy games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 2, pp. 3-18.

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

The article is devoted to modeling the system of coordination of private and public interests in promoting innovations in the organization. Subjects of controls of two levels (supervisor, agents) are taken into account. The relations between subjects are hierarchical. The algorithms for constructing equilibria in the games of Germeyer $\Gamma_{1t}, \Gamma_{2t}$ are indicated. In the study the method of qualitatively representative strategies is used. The results of a number of simulation experiments and their analysis are given.
Keywords: fuzzy cooperative game, $V$-balanced-ness, the core of a fuzzy game, TU fuzzy market game, fuzzy $LP$-game, fuzzy airport game. 
@article{MGTA_2019_11_2_a0,
     author = {Valery A. Vasil'ev},
     title = {An analog of {Bondareva--Shapley} {theorem~II.} {Examples} of $V$-balanced fuzzy games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {3--18},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2019_11_2_a0/}
}
TY  - JOUR
AU  - Valery A. Vasil'ev
TI  - An analog of Bondareva--Shapley theorem~II. Examples of $V$-balanced fuzzy games
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2019
SP  - 3
EP  - 18
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2019_11_2_a0/
LA  - ru
ID  - MGTA_2019_11_2_a0
ER  - 
%0 Journal Article
%A Valery A. Vasil'ev
%T An analog of Bondareva--Shapley theorem~II. Examples of $V$-balanced fuzzy games
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2019
%P 3-18
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2019_11_2_a0/
%G ru
%F MGTA_2019_11_2_a0
Valery A. Vasil'ev. An analog of Bondareva--Shapley theorem~II. Examples of $V$-balanced fuzzy games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 2, pp. 3-18. http://geodesic.mathdoc.fr/item/MGTA_2019_11_2_a0/

[1] Bondareva O. N., “Teoriya yadra dlya igry $n$ lits”, Vestnik LGU. Ser. mat., mekh., astron., 13:3 (1962), 141–142 | Zbl

[2] Vasilev V. A., “Analog teoremy Bondarevoi-Shepli I. Nepustota yadra nechetkoi igry”, Matematicheskaya teoriya igr i ee prilozheniya, 9:1 (2017), 3–26 | MR | Zbl

[3] Rozenmyuller I., Kooperativnye igry i rynki, Mir, M., 1974

[4] Aubin J.-P., Optima and equilibria, Springer-Verlag, Berlin–Heidelberg, 1993 | MR | Zbl

[5] Littlechild S. C., Owen G., “A simple expression for the Shapley value in a special case”, Management Science, 20 (1973), 370–372 | DOI | MR | Zbl

[6] Owen G., “On the core of linear production game”, Math. Programming, 9 (1975), 358–370 | DOI | MR | Zbl

[7] Peleg B., Sudhölter P., Introduction to the Theory of Cooperative Games, Kluwer Academic Publishers, Boston–Dordrecht–London, 2003 | MR

[8] Shapley L. S., “On balanced sets and cores”, Naval Res. Logist. Quart., 14:4 (1967), 453–460 | DOI