Peer Effects in Endogenous Networks

This paper presents a model of strategic network formation with local complementarities in effort levels and positive local externalities. Results are obtained for a general class of payoff functions, which subsumes the linear-quadratic specification frequently used in the literature. We assume homogeneous agents and characterize equilibria for two-sided and one-sided link formation. (Pairwise) Nash equilibrium networks are shown to be nested split graphs, which are a strict subset of core-periphery networks. The relevance of the convexity of the value function in obtaining these structures is highlighted. In equilibrium more central agents exert more effort and obtain higher gross payoffs. However, net of linking cost, central agents may obtain strictly lower net payoffs. Under additional assumptions on payoffs we show that the only efficient network structures are also nested split graphs. These findings are relevant for a wide range of social and economic phenomena, such as educational attainment, criminal activity, labor market participation, and R&D expenditures of firms