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: balancedness (the nucleolus is in the core), compromise stability and strong compromise admissibility (these 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 properties, we characterize the family of graphs for which the nucleolus is invariant