Provision of non-excludable public goods on networks: From equilibrium to centrality measures

We consider the provision of non-excludable public goods on a network of interdependent strategic users. We study three different equilibria of these games, namely the Nash equilibrium, socially optimal, and exit equilibrium profiles. We identify properties of the interdependence graph that guarantee the existence and uniqueness of these equilibria. We further establish a connection between users' centralities in their interdependence network, and their efforts at different interior equilibria of these games. These characterizations separate the effects of incoming and outgoing dependencies, as well as the influence of paths of different length, on users' effort levels. We discuss some conceptual and practical implications of this centrality-effort connection.