Characterizations of Network Power Measures - René van den Brink; Peter Borm; Ruud Hendrickx; Guillermo Owen (Tinbergen Institute, 2005)
A symmetric network consists of a set of positions and a set of bilateral links between these positions. Examples of such networks are exchange networks, communication networks, disease transmission networks, control networks etc. 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 beta-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 equal the well-known degree measure. We compare the beta-measure and degree measure by providing characterizations, which differ only in the normalization that is used.
Keywords: C71; Z13; 330; symmetric networks; network power; stationary power distribution; beta-measure; degree measure; Netzwerk; Graphentheorie; Kooperatives Spiel; Spieltheorie; Theorie