Geodesic
Between the prekernel and the prenucleolus
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 1 (2009) no. 1, pp. 46-66

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A collection of $TU$ games solutions intermediate between the prekernel and the prenucleolus is considered. All these solutions are Davis-Maschler consistent, symmetric and covariant. Each solution from the collection is parametrized by a positive integer $k$ such that for all games with the number of players not greater than $k$, the solution for parameter $k$ coincides with the prenucleolus, and for games with more than $k$ players it is maximal, i.e. it satisfies the "$k$-converse consistency". The properties of solutions are described and their characterization in terms of balancedness is given.
Keywords: $TU$ game, prenucleolus, consistency.
Mots-clés : prekernel 
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     author = {Ilya Katsev and Elena Yanovskaya},
     title = {Between the prekernel and the prenucleolus},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {46--66},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2009_1_1_a2/}
}
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Ilya Katsev; Elena Yanovskaya. Between the prekernel and the prenucleolus. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 1 (2009) no. 1, pp. 46-66. http://geodesic.mathdoc.fr/item/MGTA_2009_1_1_a2/