Axiomatization and Generalization of the Core for Assignment Games on the Complete Graph

Recently, assignment games, which are cooperative games derived from assignment problems, have been studied and many results on assignment games have been obtained. In this paper, we consider assignment games induced by the complete graph without assuming the graph is bipartite. First, we characterize the core of the assignment games. Second, because the core of the assignment games is not necessarily nonempty, we propose minimal negotiation sets, which are generalized solutions of the core, and research their properties.