Geodesic
Solution of the coalition game in the program strategy under uncertainty
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 2, pp. 59-67 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The abstract game models of conflict are widely used in practice in solving problems of management systems of different nature. The paper constructs a mathematical model of differential game of two coalitions with uncertainty in program strategies, considers antagonistic interaction between coalitions, defines the solutions using the principle of a guaranteed result. Application of the method of penalty functions has transformed the original maxmin problem in the related sets to the task for maximum. The paper proves the existence theorem for solutions to problems with penalties, an estimate of the error, matching conditions penalty constants and optionally-necessary condition of optimality.
Keywords: coalition game, the uncertainty, the method of penalties. 
@article{VYURV_2016_5_2_a4,
     author = {E. D. Nasonova},
     title = {Solution of the coalition game in the program strategy under uncertainty},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {59--67},
     year = {2016},
     volume = {5},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2016_5_2_a4/}
}
TY  - JOUR
AU  - E. D. Nasonova
TI  - Solution of the coalition game in the program strategy under uncertainty
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika
PY  - 2016
SP  - 59
EP  - 67
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VYURV_2016_5_2_a4/
LA  - ru
ID  - VYURV_2016_5_2_a4
ER  - 
%0 Journal Article
%A E. D. Nasonova
%T Solution of the coalition game in the program strategy under uncertainty
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika
%D 2016
%P 59-67
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/VYURV_2016_5_2_a4/
%G ru
%F VYURV_2016_5_2_a4
E. D. Nasonova. Solution of the coalition game in the program strategy under uncertainty. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 5 (2016) no. 2, pp. 59-67. http://geodesic.mathdoc.fr/item/VYURV_2016_5_2_a4/

[1] E.M. Vaysbord, “About the Coalition Differential Games”, Differential Equations, 10:4 (1974), 613–623

[2] A.F. Kleymenov, “Equilibrium Coalition Counter-Strategies in Differential Games”, Applied Mathematics and Mechanics, 46:5 (1982), 714–721

[3] V.I. Zhukovskiy, Introduction to Differential Games with Uncertainty, Publishing of MNIIPU, Moscow, 1997, 461 pp.

[4] E.V. Maksimushkina, A.F. Tarakanov, “Coalition Differential Game under Uncertainty and Stability of the Coalition Structure”, Journal of Computer and Systems Sciences International, 43:1 (2004), 72–78

[5] E.D. Baratova, A.F. Tarakanov, “The Method of Penalties and Optionally-Necessary Condition of Optimality in a Differential Cooperative Game with Uncertainty”, Universities News. Mathematics, 2004, no. 12(511), 66–74

[6] E.D. Baratova, A.F. Tarakanov, “Penalty Function Method and Necessary Conditions of Optimality in a Differential Hierarchical Game under Uncertainty”, Journal of Computer and Systems Sciences International, 42:3 (2003), 342–348

[7] Samuel Karlin, Mathematical Methods and Theory in Games, Programming and Economics, Mir, Moscow, 1964, 838 pp.

[8] V.A. Gorelik, “Maximin Problems in the Related Sets in Banach Spaces”, Cybernetics, 1983, no. 1, 64–67 pp.

[9] V.A. Gorelik, A.F. Tarakanov, “The Method of Penalties and Maximum Principle for Nonsmooth Control Problems with Variable Structure”, Cybernetics and System Analysis, 1992, no. 3, 125–130

[10] V.V. Fedorov, Numerical Methods of Maximin, Nauka, Moscow, 1979, 280 pp.