Geodesic
On a~generalization of $N$-nucleolus in cooperative games
Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 4, pp. 77-93

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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.
Keywords: TU-game, the prenucleolus, the simplified modified nucleolus, the modified nucleolus (the modiclus).
Mots-clés : solution concept 
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     author = {N. V. Smirnova and S. I. Tarashina},
     title = {On a~generalization of $N$-nucleolus in cooperative games},
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     pages = {77--93},
     publisher = {mathdoc},
     volume = {18},
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     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2011_18_4_a4/}
}
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N. V. Smirnova; S. I. Tarashina. On a~generalization of $N$-nucleolus in cooperative games. Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 4, pp. 77-93. http://geodesic.mathdoc.fr/item/DA_2011_18_4_a4/