Geodesic
Geometrical properties of the $[0,1]$-nucleolus in cooperative TU-games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 1, pp. 55-73

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In the paper we consider a new solution concept of a cooperative TU-game called the $[0,1]$-nucleolus. It is based on the ideas of the $SM$-nucleolus, the modiclus and the prenucleolus. The $[0,1]$-nucleolus takes into account both the constructive power $v(S)$ and the blocking power $v^*(S)$ of coalition $S$ with coefficients $\alpha$ and $1-\alpha$, accordingly, with $\alpha\in[0,1]$. The geometrical structure of the $[0,1]$-nucleolus is investigated. We prove that the solution consists of a finite number of sequentially connected segments in $R^n$. The $[0,1]$-nucleolus is represented by the unique point for the class of constant-sum games.
Keywords: TU-game, Kohlberg's theorem, the prenucleolus, the $SM$-nucleolus, the $[0,1]$-nucleolus.
Mots-clés : solution concept 
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     author = {Nadezhda V. Smirnova and Svetlana I. Tarashnina},
     title = {Geometrical properties of the $[0,1]$-nucleolus in cooperative {TU-games}},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
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     number = {1},
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Nadezhda V. Smirnova; Svetlana I. Tarashnina. Geometrical properties of the $[0,1]$-nucleolus in cooperative TU-games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 1, pp. 55-73. http://geodesic.mathdoc.fr/item/MGTA_2012_4_1_a3/