Directed communication in games with directed graphs

We introduce a novel concept of directed communication and a related connectedness in directed graphs, and apply this to model certain cooperation restrictions in cooperative games. In the literature on communication in directed networks or directed graphs, one can find different notions of connectedness, and different ways how directed communication restricts cooperation possibilities of players in a game. In this paper, we introduce a notion of connectedness in directed graphs that is based on directed paths. We assume that a coalition of players in a game can only cooperate if these players form a directed path in a directed communication graph. We define a restricted game following the same approach as Myerson for undirected communication situations, and consider the allocation rule that applies the Shapley value to this restricted game. We characterize this value by extended versions of the well-known component efficiency, fairness and balanced contributions axioms. Moreover, using the new notion of connectedness, we apply this allocation rule to define network centrality, efficiency and vulnerability measures for directed networks.