The nucleolus and inheritance of properties in communication situations

This paper studies the nucleolus of graph-restricted games as an alternative for the Shapley value to evaluate communication situations. We focus on the inheritance of properties of cooperative games related to the nucleolus: strong compromise admissibility and compromise stability. These two properties allow for a direct, closed formula for the nucleolus. We characterize the families of graphs for which the graph-restricted games inherit these properties from the underlying games. Moreover, for each of these two properties, we characterize the family of graphs for which the nucleolus is invariant.