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Characterizations of Network Power Measures

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Author Info
René van den Brink () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)
Peter Borm () (CentER, Tilburg University)
Ruud Hendrickx () (CentER, Tilburg University)
Guillermo Owen () (Dept. of Mathematics, Naval Postgraduate School, Monterey, Ca, USA)

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Abstract

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.

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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 05-061/1.

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Date of creation: 13 Jun 2005
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Handle: RePEc:dgr:uvatin:20050061

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: symmetric networks; network power; stationary power distribution; beta-measure; degree measure;

Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
Z13 - Other Special Topics - - Cultural Economics - - - Social Norms and Social Capital; Social Networks Economic Anthropology

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Borm, P. & Brink, R. van den & Slikker, M., 2000. "An iterative procedure for evaluating digraph competitions," Research Memorandum 788, Tilburg University, Faculty of Economics and Business Administration. [Downloadable!]
  2. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December. [Downloadable!] (restricted)
  3. Hendrickx, Ruud & Borm, Peter & Brink, Rene van den & Owen, Guillermo, 2005. "The V L value for network games," Discussion Paper 65, Tilburg University, Center for Economic Research. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Hendrickx, Ruud & Borm, Peter & Brink, Rene van den & Owen, Guillermo, 2005. "The V L value for network games," Discussion Paper 65, Tilburg University, Center for Economic Research. [Downloadable!]
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This page was last updated on 2009-11-19.

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