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Article

Геометрические свойства [0,1]-N-ядра

Смирнова Н. В., Тарашнина С. И.

In the paper we consider a new solution concept of a cooperative TU-game called the [0,1]-nucleolus. It is based on the  ideas of the SM-nucleolus, the modiclus and the prenucleolus. The [0,1]-nucleolus takes into account both the constructive power v(S) and the blocking power v*(S) of coalition S  with coefficients alpha and 1-alpha, accordingly, with alpha\in[0,1]. The geometrical structure of the [0,1]-nucleolus is investigated. We prove the solution consists of a finite number  of sequentally connected segments in R^{n}. The [0,1]-nucleolus is represented by the unique point for the class of constant-sum games.