Gately Values of Cooperative Games

TL;DR

This paper explores Gately's solution for cooperative games, generalizes it with a parameter, and examines its relationship with other solution concepts like the Core, Nucleolus, and Shapley value.

Contribution

It introduces a parameterized generalization of Gately's solution and analyzes its properties and relationships with established solution concepts.

Findings

Gately's solution is in the Core for all regular 3-player games.

Conditions are identified when Gately values are Core imputations.

The relationship between Gately value and Shapley value is analyzed.

Abstract

We investigate Gately's solution concept for cooperative games with transferable utilities. Gately's conception introduced a bargaining solution that minimises the maximal quantified ``propensity to disrupt'' the negotiation process 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 also 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 and the Nucleolus and show that Gately's solution is in the Core for all regular 3-player games. We identify exact conditions under which generally these Gately values are Core imputations for arbitrary regular cooperative games. Finally, we investigate the relationship of the Gately value with the Shapley value.