Geodesic
On stability for a finite cooperative game with a generalized concept of equilibrium
Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 47-55 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a finite cooperative game in the normal form with a parametric principle of optimality (the generalized concept of equilibrium). This principle is defined by the partitioning of the players into coalitions. In this situation, two extreme cases of this partitioning correspond to the lexicographically optimal situation and the Nash equilibrium situation, respectively. The analysis of stability for a set of generalized equilibrium situations under the perturbations of the coefficients of the linear payoff functions is performed. 
@article{TIMB_2007_15_1_a5,
     author = {E. Gurevsky and V. A. Emelichev and A. A. Platonov},
     title = {On stability for a finite cooperative game with a generalized concept of equilibrium},
     journal = {Trudy Instituta matematiki},
     pages = {47--55},
     year = {2007},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a5/}
}
TY  - JOUR
AU  - E. Gurevsky
AU  - V. A. Emelichev
AU  - A. A. Platonov
TI  - On stability for a finite cooperative game with a generalized concept of equilibrium
JO  - Trudy Instituta matematiki
PY  - 2007
SP  - 47
EP  - 55
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a5/
LA  - ru
ID  - TIMB_2007_15_1_a5
ER  - 
%0 Journal Article
%A E. Gurevsky
%A V. A. Emelichev
%A A. A. Platonov
%T On stability for a finite cooperative game with a generalized concept of equilibrium
%J Trudy Instituta matematiki
%D 2007
%P 47-55
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a5/
%G ru
%F TIMB_2007_15_1_a5
E. Gurevsky; V. A. Emelichev; A. A. Platonov. On stability for a finite cooperative game with a generalized concept of equilibrium. Trudy Instituta matematiki, Tome 15 (2007) no. 1, pp. 47-55. http://geodesic.mathdoc.fr/item/TIMB_2007_15_1_a5/

[1] Mulen E., Teoriya igr, M., 1985 | MR | Zbl

[2] Petrosyan L.A., Zenkevich N.A., Semina E.A., Teoriya igr, M., 1998 | MR

[3] Bukhtoyarov S.E., Emelichev V.A., “Konechnye koalitsionnye igry: parametrizatsiya printsipa optimalnosti (“ot Pareto do Nesha”) i ustoichivost obobschenno-effektivnykh situatsii”, Dokl. NAN Belarusi, 46:6 (2002), 36–38 | MR | Zbl

[4] Bukhtoyarov S.E., Emelichev V.A., Stepanishina Yu.V., “Voprosy ustoichivosti vektornykh diskretnykh zadach s parametricheskim printsipom optimalnosti”, Kibernetika i sistemnyi analiz, 2003, no. 4, 155–166 | MR | Zbl

[5] Emelichev V.A., Kuzmin K.G., “Konechnye koalitsionnye igry s parametricheskoi kontseptsiei ravnovesiya v usloviyakh neopredelennosti”, Izv. RAN. Teoriya i sistemy upravleniya, 2006, no. 2, 117–122 | MR

[6] Bukhtoyarov S.E., Emelichev V.A., “Mera ustoichivosti konechnoi koalitsionnoi igry s parametricheskim (“ot Pareto do Nesha”) printsipom optimalnosti”, Zhurnal vychisl. matematiki i matem. fiziki, 46:7 (2006), 1258–1264 | MR

[7] Podinovskii V.V., Gavrilov V.M., Optimizatsiya po posledovatelno primenyaemym kriteriyam, M., 1975

[8] Chervak Yu.Yu., Optimizatsiya. Nepokraschuvanii vibir, Uzhgorod, 2002

[9] Nesh Dzh., “Beskoalitsionnye igry”, Matrichnye igry, M., 1961

[10] Sotskov Yu.N., Leontev V.K., Gordeev E.N., “Some concepts of stability analysis in combinatorial optimization”, Discrete Appl. Math., 58:2 (1995), 169–190 | DOI | MR | Zbl

[11] Emelichev V.A., Girlich E., Nikulin Yu.V., Podkopaev D.P., “Stability and regularization of vector problems of integer linear programming”, Optimization, 51:4 (2002), 645–676 | DOI | MR | Zbl

[12] Bukhtoyarov S.E., Kuzmin K.G., “On stability in game problems of finding Nash set”, Computer Science J. of Moldova, 12:3 (2004), 381–388 | MR