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Game Theoretic Foundations of the Gately Power Measure for Directed Networks

Author

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  • Robert P. Gilles

    (Department of Economics, The Queen’s University of Belfast, Riddel Hall, 185 Stranmillis Road, Belfast BT9 5EE, UK)

  • Lina Mallozzi

    (Department of Mathematics and Applications, University of Naples Federico II, Via Claudio 21, 80125 Naples, Italy)

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 embedded within a hierarchical network can be represented through appropriate TU-games. We investigate the properties of these TU-representations 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 β -measure, and construct an axiomatisation of the Gately measure.

Suggested Citation

  • Robert P. Gilles & Lina Mallozzi, 2023. "Game Theoretic Foundations of the Gately Power Measure for Directed Networks," Games, MDPI, vol. 14(5), pages 1-19, September.
    • Handle: RePEc:gam:jgames:v:14:y:2023:i:5:p:64-:d:1247926
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    References listed on IDEAS

    as
    1. Robert P. Gilles & Lina Mallozzi, 2022. "Gately Values of Cooperative Games," Papers 2208.10189, arXiv.org, revised Jul 2023.
    2. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, March.
    3. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
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    8. 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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