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Properties of solutions of cooperative games with transferable utilities


We understand a solution of a cooperative TU-game as the α-prenucleoli set, αR, 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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Correspondence to N. V. Smirnova.

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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).

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  • TU-game
  • prenucleolus
  • SM-nucleolus
  • [0, 1]-prenucleolus
  • α-prenucleoli set
  • duality