Estimating local interactions among many agents who observe their neighbors

In various economic environments, people observe other people with whom they strategically interact. We can model such information-sharing relations as an information network, and the strategic interactions as a game on the network. When any two agents in the network are connected either directly or indirectly in a large network, empirical modeling using an equilibrium approach can be cumbersome, since the testable implications from an equilibrium generally involve all the players of the game, whereas a researcher's data set may contain only a fraction of these players in practice. This paper develops a tractable empirical model of linear interactions where each agent, after observing part of his neighbors' types, not knowing the full information network, uses best responses that are linear in his and other players' types that he observes, based on simple beliefs about the other players' strategies. We provide conditions on information networks and beliefs such that the best responses take an explicit form with multiple intuitive features. Furthermore, the best responses reveal how local payoff interdependence among agents is translated into local stochastic dependence of their actions, allowing the econometrician to perform asymptotic inference without having to observe all the players in the game or having to know the precise sampling process.