Many-Player Asymptotics for Estimating Models of Network Formation: Konrad Menzel (NYU)

Abstract: We consider a random utility model of strategic network formation, where we derive a tractable approximation to the distribution of network links using many-player asymptotics. Our framework assumes that agents have heterogeneous tastes over links, and allows for anonymous and non-anonymous interaction effects among links. The observed network is assumed to be pairwise stable, and we impose no restrictions regarding selection among multiple stable outcomes. Our main results concern convergence of the link frequency distribution from finite pairwise stable networks to the (many-player) limiting distribution. The set of possible limiting distributions is shown to have a fairly simple form and is characterized through aggregate equilibrium conditions, which may permit multiple solutions. We analyze identification of link preferences and propose a method for estimation of preference parameters. We also derive an analytical expression for agents’ welfare (expected surplus) from the structure of the network.