Two-step values for games with two-level communication structure

Sylvain Béal, Anna Khmelnitskaya (Corresponding Author), Philippe Solal

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    Abstract

    TU games with two-level communication structure, in which a two-level communication structure relates fundamentally to the given coalition structure and consists of a communication graph on the collection of the a priori unions in the coalition structure, as well as a collection of communication graphs within each union, are considered. For such games we introduce two families of two-step values inspired by the two-step procedures staying behind the Owen value (Owen, in: Henn, Moeschlin (eds) Essays in mathematical economics and game theory, Springer, Berlin, pp 76–88, 1977) and the two-step Shapley value (Kamijo in Int Game Theory Rev 11:207–214, 2009) for games with coalition structure. Our approach is based on the unified treatment of several component efficient values for games with communication structure and it generates two-stage solution concepts that apply component efficient values for games with communication structure on both distribution levels. Comparable axiomatic characterizations are provided.
    Original languageEnglish
    Pages (from-to)563-587
    Number of pages25
    JournalJournal of combinatorial optimization
    Volume35
    Issue number2
    Early online date1 Nov 2017
    DOIs
    Publication statusPublished - Feb 2018

    Keywords

    • UT-Hybrid-D
    • Owen value
    • Two-step Shapley value
    • Component efficiency
    • Deletion link property
    • TU game with two-level communication structure

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