Abstract
We understand a solution of a cooperative TU-game as the α-prenucleoli set, α ∈ R, which is a generalization of the notion of the [0, 1]-prenucleolus. We show that the set of all α-nucleoli takes into account the constructive power with the weight α and the blocking power with the weight (1 − α) for all possible values of the parameter α. The further generalization of the solution by introducing two independent parameters makes no sense. We prove that the set of all α-prenucleoli satisfies properties of duality and independence with respect to the excess arrangement. For the considered solution we extend the covariance propertywith respect to strategically equivalent transformations.
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Original Russian Text © N.V. Smirnova, S.I. Tarashnina, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 6, pp. 73–85.
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Smirnova, N.V., Tarashnina, S.I. Properties of solutions of cooperative games with transferable utilities. Russ Math. 60, 63–74 (2016). https://doi.org/10.3103/S1066369X16060086
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DOI: https://doi.org/10.3103/S1066369X16060086