What goes around comes around: A theory of indirect reciprocity in networks

We consider strategic interaction on a network of heterogeneous long-term relationships. The bilateral relationships are independent of each other in terms of actions and realized payoffs, and we assume that information regarding outcomes is private to the two parties involved. In spite of this, the network can induce strategic interdependencies between relationships, which facilitate efficient outcomes. We derive necessary and sufficient conditions that characterize efficient equilibria of the network game in terms of the architecture of the underlying network, and interpret these structural conditions in light of empirical regularities observed in many social and economic networks.