Characterizations of the Beta and the Degree Network Power Measure

J.R. van den Brink, P. Borm, R. Hendrickx, G. Owen

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    Abstract

    A symmetric network consists of a set of positions and a set of bilateral links between these positions. For every symmetric network we define a cooperative transferable utility game that measures the "power" of each coalition of positions in the network. Applying the Shapley value to this game yields a network power measure, the β-measure, which reflects the power of the individual positions in the network. Applying this power distribution method iteratively yields a limit distribution, which turns out to be proportional to the well-known degree measure. We compare the β-measure and degree measure by providing characterizations, which differ only in the normalization that is used. © 2007 Springer Science+Business Media LLC.
    Original languageEnglish
    Pages (from-to)519-536
    JournalTheory and Decision
    Volume64
    DOIs
    Publication statusPublished - 2008

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