Game theoretic foundations of the gately power measure for directed networks - Robert Paul Gilles; Lina Mallozzi (Games, 2023)
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: A14; C71; D20; 330; cooperative game; authority network; network centrality measure; Gately measure; axiomatisation