Generalised Gately Values of Cooperative Games

We investigate Gately's solution concept for cooperative games with transferable utilities. Gately's conception is a bargaining solution and minimises the maximal quantified 'propensity to disrupt' the negotiation of the players over the allocation of the generated collective payoffs. Gately's solution concept is well-defined for a broad class of games. We consider a generalisation based on a parameter-based quantification of the propensity to disrupt. Furthermore, we investigate the relationship of these generalised Gately values with the Core. Gately's solution is in the Core for all regular 3-player games. We identify precise conditions under which generalised Gately values are Core imputations for arbitrary regular cooperative games. We devise an axiomatisation of the Gately value for the class of regular cooperative games. We conclude the paper with an application of the Gately value to the measurement of power in hierarchical social networks.