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Game theoretic foundations of the Gately power measure for directed networks

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  • Robert P. Gilles
  • Lina Mallozzi

Abstract

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players--constituting a hierarchical network. The power distribution of a hierarchical network can be represented through a TU-game. We investigate the properties of this TU-representation and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a Core power gauge, investigate the relationship of the Gately with the $\beta$-measure, and construct an axiomatisation of the Gately measure.

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  • Robert P. Gilles & Lina Mallozzi, 2023. "Game theoretic foundations of the Gately power measure for directed networks," Papers 2308.02274, arXiv.org.
    • Handle: RePEc:arx:papers:2308.02274
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    References listed on IDEAS

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    1. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, December.
    2. Gately, Dermot, 1974. "Sharing the Gains from Regional Cooperation: A Game Theoretic Application to Planning Investment in Electric Power," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 195-208, February.
    3. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    4. Jochen Staudacher & Johannes Anwander, 2019. "Conditions for the uniqueness of the Gately point for cooperative games," Papers 1901.01485, arXiv.org.
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    Cited by:

    1. Robert P. Gilles & Lina Mallozzi, 2025. "Gately values of cooperative games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(3), pages 723-758, May.

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