Graph value for cooperative games

We suppose that players in a cooperative game are located within a graph structure, such as a social network or supply route, that limits coalition formation to coalitions along connected paths within the graph. This leads to a generalisation of the Shapley value that is studied here from an axiomatic perspective. The resulting ‘graph value’ is endogenously asymmetric, with the automorphism group of the graph playing a crucial role in determining the relative values of players.