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Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2009, Volume 1, Issue 1, Pages 46–66
(Mi mgta3)
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Between the prekernel and the prenucleolus
Ilya Katsev, Elena Yanovskaya St. Petersburg Institute for Economics and Mathematics RAS, St. Petersburg
Abstract:
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, prekernel, prenucleolus, consistency.
Citation:
Ilya Katsev, Elena Yanovskaya, “Between the prekernel and the prenucleolus”, Mat. Teor. Igr Pril., 1:1 (2009), 46–66
Linking options:
https://www.mathnet.ru/eng/mgta3 https://www.mathnet.ru/eng/mgta/v1/i1/p46
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