Geometrical properties of the $[0,1]$-nucleolus in cooperative TU-games

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 that the solution consists of a finite number of sequentially connected segments in $R^n$. The $[0,1]$-nucleolus is represented by the unique point for the class of constant-sum games.