Social learning and aggregate network uncertainty

Abstract

We study the perfect Bayesian equilibria of a model of social learning in networks where agents learn about an unknown state of the world by observing the actions of their neighbors. The network topology is drawn from an arbitrary distribution; contrary to prior models in the literature, two agents' sets of neighbors are not assumed to be independent. This extension allows us to capture real-world network phenomena, such as clustering and assortativity, and to consider the performance of social learning in widely used models of social networks, such as preferential attachment models. Since agents only observe the realization of their own neighborhoods, two agents could have vastly different beliefs about the overall network structure, and they may disagree over who is well-informed or well-connected. We call this phenomenon aggregate network uncertainty. This greatly alters our understanding of social learning dynamics and whether networks successfully aggregate dispersed information. Past literature has focused on herding outcomes as the key inefficiency of social learning, but we find that more severe inefficiencies can occur. In addition to the traditional metric of information aggregation, we introduce a second, weaker metric motivated by the notion of an expert, which we define as an outside agent whose private information is at least as strong as that of any other agent in the network. Learning is successful by our metric if all agents perform at least as well as an expert in the limit as society grows. Without aggregate network uncertainty, information aggregation is successful by this metric if and only if a connectivity condition holds. Herding outcomes can only occur once social learning has met our metric of success. With aggregate network uncertainty, there are several ways learning fails to reach even this weaker metric. Our main positive result is a characterization of sufficient conditions for successful information aggregation in the presence of aggregate network uncertainty. We show that information aggregation is successful whenever agents can identify well-connected neighbors with low distortion. Since neighborhoods are correlated, observing an agent may alter the informativeness of that agent's decision; distortion measures the extent to which this phenomenon occurs. We also demonstrate that in special cases our conditions are both necessary and sufficient for successful learning. We use this characterization to show that the popular preferential attachment network model successfully aggregates information.