Title: Estimating Local Interactions Among Many Agents Who Observe Their Neighbors,
Abstract: In various economic environments, people observe those 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,
empirical modeling using an equilibrium approach is 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
other players' strategies. We provide conditions on information networks and
beliefs such that 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
precisely the sampling process.