Game Theoretic Foundations of the Gately Power Measure for Directed Networks

Robert P. Gilles and Lina Mallozzi ()
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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

Games, 2023, vol. 14, issue 5, 1-19

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.

Keywords: cooperative game; authority network; network centrality measure; Gately measure; axiomatisation (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2023
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