Geodesic
Multicriteria coalitional model of decision-making over the set of projects with constant payoff matrix in the noncooperative game
Contributions to game theory and management, Tome 7 (2014), pp. 93-103.

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

Let $N$ be the set of players and $M$ the set of projects. The multicriteria coalitional model of decision-making over the set of projects is formalized as family of games with different fixed coalitional partitions for each project that required the adoption of a positive or negative decision by each of the players. The players' strategies are decisions about each of the project. The vector-function of payoffs for each player is defined on the set situations in the initial noncooperative game. We reduce the multicriteria noncooperative game to a noncooperative game with scalar payoffs by using the minimax method of multicriteria optimization. Players forms coalitions in order to obtain higher income. Thus, for each project a coalitional game is defined. In each coalitional game it is required to find in some sense optimal solution. Solving successively each of the coalitional games, we get the set of optimal $n$-tuples for all coalitional games. It is required to find a compromise solution for the choice of a project, i. e. it is required to find a compromise coalitional partition. As an optimality principles are accepted generalized PMS-vector (Grigorieva and Mamkina, 2009; Petrosjan and Mamkina, 2006) and its modifications, and compromise solution.
Keywords: coalitional game, PMS-vector, compromise solution, multicriteria model. 
@article{CGTM_2014_7_a8,
     author = {Xeniya Grigorieva},
     title = {Multicriteria coalitional model of decision-making over the set of projects with constant payoff matrix in the noncooperative game},
     journal = {Contributions to game theory and management},
     pages = {93--103},
     publisher = {mathdoc},
     volume = {7},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2014_7_a8/}
}
TY  - JOUR
AU  - Xeniya Grigorieva
TI  - Multicriteria coalitional model of decision-making over the set of projects with constant payoff matrix in the noncooperative game
JO  - Contributions to game theory and management
PY  - 2014
SP  - 93
EP  - 103
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CGTM_2014_7_a8/
LA  - en
ID  - CGTM_2014_7_a8
ER  - 
%0 Journal Article
%A Xeniya Grigorieva
%T Multicriteria coalitional model of decision-making over the set of projects with constant payoff matrix in the noncooperative game
%J Contributions to game theory and management
%D 2014
%P 93-103
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CGTM_2014_7_a8/
%G en
%F CGTM_2014_7_a8
Xeniya Grigorieva. Multicriteria coalitional model of decision-making over the set of projects with constant payoff matrix in the noncooperative game. Contributions to game theory and management, Tome 7 (2014), pp. 93-103. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a8/

[1] Grigorieva X., Mamkina S., “Solutions of Bimatrix Coalitional Games”, GTM'2008, Collected papers printed on the Second International Conference “Game Theory and Management”, Contributions to game and management, eds. Leon A. Petrosjan, Nikolay A. Zenkevich, Graduate School of Management, SpbSU, SPb., 2009, 147–153 | MR | Zbl

[2] Petrosjan L., Mamkina S., “Dynamic Games with Coalitional Structures”, Intersectional Game Theory Review, 8:2 (2006), 295–307 | DOI | MR | Zbl

[3] Nash J., “Non-cooperative Games”, Ann. Mathematics, 54 (1951), 286–295 | DOI | MR | Zbl

[4] Shapley L. S., “A Value for $n$-Person Games”, Contributions to the Theory of Games, eds. Kuhn H. W., Tucker A. W., Princeton University Press, 1953, 307–317 | MR

[5] Grigorieva X. V., “Dynamic approach with elements of local optimization in a class of stochastic games of coalition”, Interuniversity thematic collection of works of St. Petersburg State University of Civil Engineering, v. 16, ed. B. G. Wager, 2009, 104–138

[6] Malafeyev O. A., Control system of conflict, St. Petersburg State University, SPb., 2001