Generalised Gately Values of Cooperative Games
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We investigate Gately's solution concept for cooperative games with transferable utilities. Gately's solution conception is a bargaining solution and tries to minimise the maximal quantified "propensity to disrupt" the negotiation of the players over the allocation of the generated collective payoffs. We show that 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 Gately's solution and its generalisation with the Core. We show that Gately's solution is in the Core for all regular 3-player games. We also identify precise conditions under which generalised Gately values are Core imputations for arbitrary regular cooperative games. We construct the dual of generalised Gately values and devise an axiomatisation of these values 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.
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