Inheritance of properties in communication situations

In this paper we consider cooperative games in which the possibilities for cooperation between the players are restricted because communication betwee n the players is restricted. The bilateral communication possibilities are modeled by means of a (communication) graph. We are interested in how the c ommunication restrictions influence the game. In particular, we investigate what conditions on the communication graph guarantee that certain appealin g properties of the original game are inherited by the graph-restricted gam e, the game that arises once the communication restrictions are taken into account. We study inheritance of the following properties: average convexit y, inclusion of the Shapley value in the core, inclusion of the Shapley val ues of a game and all its subgames in the corresponding cores, existence of a population monotonic allocation scheme, and the property that the extend ed Shapley value is a population monotonic allocation scheme.