This article is cited in 2 scientific papers (total in 2 papers)
On a generalization of $N$-nucleolus in cooperative games
N. V. Smirnovaab, S. I. Tarashinaba
a Saint-Petersburg State University, Saint-Petersburg, Russia
b International Banking Institute, Saint-Petersburg, Russia
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.
TU-game, solution concept, the prenucleolus, the simplified modified nucleolus, the modified nucleolus (the modiclus).
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N. V. Smirnova, S. I. Tarashina, “On a generalization of $N$-nucleolus in cooperative games”, Diskretn. Anal. Issled. Oper., 18:4 (2011), 77–93
Citation in format AMSBIB
\by N.~V.~Smirnova, S.~I.~Tarashina
\paper On a~generalization of $N$-nucleolus in cooperative games
\jour Diskretn. Anal. Issled. Oper.
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This publication is cited in the following articles:
Nadezhda V. Smirnova, Svetlana I. Tarashnina, “Geometricheskie svoistva $[0,1]$-$N$-yadra v kooperativnykh TP-igrakh”, MTIP, 4:1 (2012), 55–73
N. V. Smirnova, S. I. Tarashnina, “On properties of solutions of cooperative TU-games”, Russian Math. (Iz. VUZ), 60:6 (2016), 63–74
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