Network formation and heterogeneous risks

We introduce a novel, tractable model with two types of agents interacting in a social or economic network. The first type of linkage benefits both directly and indirectly connected agents, whereas the second benefits direct connections but harms indirect ones. This framework has broad applications, including financial networks with banks and borrowing firms, production networks with sustainable and polluting firms, and social networks where interactions affect disease spread. We study how the linkages formed with one type of agents are affected by the connections with other types. To this end, we characterize the socially efficient network, in which banks form large connected components with few borrowers. In contrast, the equilibrium network features more borrowers per bank and smaller bank components. A key driver of this outcome is the cross-relationship externalities which can affect the sign of inefficiency across types of relationships. This opens the door for significant policy interventions, reshaping the architecture of the networks obtained in equilibrium in novel ways. We also analyze heterogeneity and information asymmetries among agents and show that both amplify the negative effects of these externalities.