On the <Emphasis Type="Italic">k</Emphasis>-accessibility of cores of <Emphasis Type="Italic">TU</Emphasis>-cooperative games |
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Authors: | V A Vasil’ev |
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Affiliation: | 1.Sobolev Institute of Mathematics,Siberian Branch of the Russian Academy of Sciences,Novosibirsk,Russia |
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Abstract: | This paper proposes a strengthening of the author’s core-accessibility theorem for balanced TU-cooperative games. The obtained strengthening relaxes the influence of the nontransitivity of classical domination αv on the quality of the sequential improvement of dominated imputations in a game v. More specifically, we establish the k-accessibility of the core C(α v ) of any balanced TU-cooperative game v for all natural numbers k: for each dominated imputation x, there exists a converging sequence of imputations x0, x1,..., such that x0 = x, lim x r ∈ C(α v ) and xr?m is dominated by any successive imputation x r with m ∈ 1, k] and r ≥ m. For showing that the TU-property is essential to provide the k-accessibility of the core, we give an example of an NTU-cooperative game G with a ”black hole” representing a nonempty closed subset B ? G(N) of dominated imputations that contains all the α G -monotonic sequential improvement trajectories originating at any point x ∈ B. |
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