Multicriteria Coalitional Model of Decision-making over the Set of Projects with Constant Payoff Matrix in the Noncooperative Game

Xeniya Grigorieva

Authors

Xeniya Grigorieva Saint Petersburg State University

Abstract

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

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References

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