Geodesic
On a~generalization of $N$-nucleolus in cooperative games
Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 4, pp. 77-93.

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

We describe a new solution concept for a cooperative TU-game, called the $[0,1]$-nucleolus. It is based on the ideas of the nucleolus and the simplified modified nucleolus. The $[0,1]$-nucleolus takes into account both the constructive and the blocking powers of a coalition with all possible ratios between them. We show that this solution satisfies the following properties: nonemptiness (NE), covariance property (COV), anonimity (AN), Pareto optimality (PO), reasonableness (RE), and dummy player (DUM). Moreover, the $[0,1]$-nucleolus satisfies the individual rationality property (IR) for the class of 0-monotonic games and the single valued property (SIVA) for the class of constant-sum games. We also investigate connection between the $[0,1]$-nucleolus and some well-known solutions of cooperative TU-games such as the Shapley value, the prenucleolus, the simplified modified nucleolus and the modiclus. Tabl. 1, ill. 1, bibliogr. 8.
Keywords: TU-game, the prenucleolus, the simplified modified nucleolus, the modified nucleolus (the modiclus).
Mots-clés : solution concept 
@article{DA_2011_18_4_a4,
     author = {N. V. Smirnova and S. I. Tarashina},
     title = {On a~generalization of $N$-nucleolus in cooperative games},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {77--93},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2011_18_4_a4/}
}
TY  - JOUR
AU  - N. V. Smirnova
AU  - S. I. Tarashina
TI  - On a~generalization of $N$-nucleolus in cooperative games
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2011
SP  - 77
EP  - 93
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2011_18_4_a4/
LA  - ru
ID  - DA_2011_18_4_a4
ER  - 
%0 Journal Article
%A N. V. Smirnova
%A S. I. Tarashina
%T On a~generalization of $N$-nucleolus in cooperative games
%J Diskretnyj analiz i issledovanie operacij
%D 2011
%P 77-93
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2011_18_4_a4/
%G ru
%F DA_2011_18_4_a4
N. V. Smirnova; S. I. Tarashina. On a~generalization of $N$-nucleolus in cooperative games. Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 4, pp. 77-93. http://geodesic.mathdoc.fr/item/DA_2011_18_4_a4/

[1] Pecherskii S. L., Yanovskaya E. B., Kooperativnye igry: resheniya i aksiomy, Izd-vo Evrop. un-ta v Sankt-Peterburge, SPb., 2004, 456 pp.

[2] Maschler M., “The bargaining set, kernel, and nucleolus: a survey”, Handbook of game theory, v. 1, Elsevier Sci. Publ. BV, Berlin, 1992, 591–665 | MR

[3] Maschler M., Peleg B., Shapley L. S., “Geometric properties of the kernel, nucleolus and related solution concepts”, Math. Oper. Res., 4 (1979), 303–338 | DOI | MR | Zbl

[4] Scarf H., “The core of an $N$ person game”, Econometrica, 35 (1967), 50–69 | DOI | MR | Zbl

[5] Schmeidler D., “The nucleolus of a characteristic function game”, SIAM J. Appl. Math., 17 (1969), 1163–1170 | DOI | MR | Zbl

[6] Shapley L. S., “A value for $n$-person games”, Contributions to the theory of games, v. II, Princeton Univ. Press, Princeton, 1953, 307–317 | MR

[7] Sudhölter P., “The modified nucleolus: properties and axiomatizations”, Int. J. Game Theory, 26 (1997), 147–182 | DOI | MR

[8] Tarashnina S., “The simplified modified nucleolus of a cooperative TU-game”, TOP: Oper. Res. Decision Theory, 19:1 (2011), 150–166