Geodesic
On monotonicity of the SM-nucleolus and the $\alpha$-nucleolus
Contributions to game theory and management, Tome 7 (2014), pp. 8-16

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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.
Keywords: cooperative TU-game, solution concept, aggregate and coalitional monotonicity, the SM-nucleolus, the $\alpha$-nucleolus. 
@article{CGTM_2014_7_a1,
     author = {Sergey V. Britvin and Svetlana I. Tarashnina},
     title = {On monotonicity of the {SM-nucleolus} and the $\alpha$-nucleolus},
     journal = {Contributions to game theory and management},
     pages = {8--16},
     publisher = {mathdoc},
     volume = {7},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2014_7_a1/}
}
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Sergey V. Britvin; Svetlana I. Tarashnina. On monotonicity of the SM-nucleolus and the $\alpha$-nucleolus. Contributions to game theory and management, Tome 7 (2014), pp. 8-16. http://geodesic.mathdoc.fr/item/CGTM_2014_7_a1/