Games on Networks: Direct Complements and Indirect Substitutes

Abstract

We study linear quadratic games played on a network where strategies are complements between neighbors and substitutes between agents at distance-two. We provide micro-founded problems where this pattern of interaction is due to a local congestion effect. Equilibrium behavior systematically differs from a model of peer effects only. First, the ranking of equilibrium actions may not follow that of network centralities, with large behavior prevailing at the periphery of the network. Second, network density affects aggregate behavior in a non-monotonic way. Third, segregating agents according to their preferences has a non-monotonic effect on the polarization of behavior. We relate these patterns to evidence from smoking networks, industrial districts and ethnically fragmented societies. We conclude by discussing the implications for the identification of peer effects.