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On the k-accessibility of cores of TU-cooperative games

  • Mathematical Game Theory and Applications
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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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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    V. A. Vasil’ev

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  1. V. A. Vasil’ev
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Correspondence to V. A. Vasil’ev.

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Original Russian Text © V.A. Vasil’ev, 2016, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2016, No. 2, pp. 3–27.

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Vasil’ev, V.A. On the k-accessibility of cores of TU-cooperative games. Autom Remote Control 78, 2248–2264 (2017). https://doi.org/10.1134/S000511791712013X

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  • DOI: https://doi.org/10.1134/S000511791712013X

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