Game Theoretic Foundations of the Gately Power Measure for Directed Networks

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