Characterizations of the β- and the Degree Network Power Measure

Theory and Decision 64 (4):519-536 (2008)
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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.

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