Static Model of Decision-Making over the Set of Coalitional Partitions

Xeniya Grigorieva

Authors

Xeniya Grigorieva Saint Petersburg State University

Abstract

Let be N the set of players and M the set of projects. The 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. Players can form 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

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References

Grigorieva, X., Mamkina, S. (2009). Solutions of Bimatrix Coalitional Games. Contributions to game and management. Collected papers printed on the Second International Conference “Game Theory and Management” [GTM’2008]/ Edited by Leon A. Petrosjan, Nikolay A. Zenkevich. -SPb.: Graduate School of Management, SpbSU, 2009, pp. 147–153.

Petrosjan, L., Mamkina, S. (2006). Dynamic Games with Coalitional Structures. Intersectional Game Theory Review, 8(2), 295–307.

Nash, J. (1951). Non-cooperative Games. Ann. Mathematics 54, 286–295.

Shapley, L.S. (1953). A Value for n-Person Games. In: Contributions to the Theory of Games( Kuhn, H.W. and A.W. Tucker, eds.), pp. 307–317. Princeton University Press.

Grigorieva, X.V. (2009). Dynamic approach with elements of local optimization in a class of stochastic games of coalition. In: Interuniversity thematic collection of works of St. Petersburg State University of Civil Engineering (Ed. Dr., prof. B. G. Wager). Vol. 16. Pp. 104–138.

Malafeyev, O.A. (2001). Control system of conﬂict. -SPb.: St. Petersburg State University, 2001.