On a generalization of $N$-nucleolus in cooperative games

We describe a new solution concept for a cooperative TU-game, called the $[0,1]$-nucleolus. It is based on the ideas of the nucleolus and the simplified modified nucleolus. The $[0,1]$-nucleolus takes into account both the constructive and the blocking powers of a coalition with all possible ratios between them. We show that this solution satisfies the following properties: nonemptiness (NE), covariance property (COV), anonimity (AN), Pareto optimality (PO), reasonableness (RE), and dummy player (DUM). Moreover, the $[0,1]$-nucleolus satisfies the individual rationality property (IR) for the class of 0-monotonic games and the single valued property (SIVA) for the class of constant-sum games. We also investigate connection between the $[0,1]$-nucleolus and some well-known solutions of cooperative TU-games such as the Shapley value, the prenucleolus, the simplified modified nucleolus and the modiclus. Tabl. 1, ill. 1, bibliogr. 8.