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Characterizations of Network Power Measures

Author

Listed:
  • 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)

Abstract

This discussion paper led to a publication in 'Theory and Decision', 2008, 64, 519-536. 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.

Suggested Citation

  • René van den Brink & Peter Borm & Ruud Hendrickx & Guillermo Owen, 2005. "Characterizations of Network Power Measures," Tinbergen Institute Discussion Papers 05-061/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050061
    as

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    File URL: https://papers.tinbergen.nl/05061.pdf
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    References listed on IDEAS

    as
    1. Peter Borm & René van den Brink & Marco Slikker, 2002. "An Iterative Procedure for Evaluating Digraph Competitions," Annals of Operations Research, Springer, vol. 109(1), pages 61-75, January.
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    Cited by:

    1. Hendrickx, R.L.P. & Borm, P.E.M. & van den Brink, J.R. & Owen, G., 2005. "The V L Value for Network Games," Discussion Paper 2005-65, Tilburg University, Center for Economic Research.

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    More about this item

    Keywords

    symmetric networks; network power; stationary power distribution; beta-measure; degree measure;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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