On monotonicity of the SM-nucleolus and the $\alpha$-nucleolus

In this paper two single-valued solution concepts of a TU-game with a finite set of players, the SM-nucleolus and the $\alpha$-nucleolus, are considered. Based on the procedure of finding lexicographical minimum, there was proposed an algorithm allowing to calculate the SM-nucleolus as well as the prenucleolus. This algorithm is modified to calculate the $\alpha$-nucleolus for any fixed $\alpha \in [0,1]$. Using this algorithm the monotonicity properties of the SM-nucleolus and the $\alpha$-nucleolus are studied by means of counterexamples.