Social Learning and Network Uncertainty

Abstract

We study the perfect Bayesian equilibria of a sequential model of social learning in networks where agents learn about a state of the world by observing the actions of their neighbors. In contrast with prior work, we do not assume that the agents' sets of neighbors are mutually independent. We introduce a new, weaker metric of social learning, information diffusion, that captures whether the agents eventually perform as well as if they had received the strongest possible private signals. We show that information diffusion is always attained if the neighborhoods are independently drawn, as long as a minimal connectivity condition is satisfied. However, we show that failures of information diffusion do occur when neighborhoods are correlated. We then provide two sufficient conditions for successful information diffusion. We show first that information diffuses whenever agents can identify well-connected neighbors with low distortion, a condition that ensures that observing a decision does not greatly alter its informativeness. This characterization allows us to establish positive learning results for a preferential attachment network. We also show that information diffuses whenever the network topology can be represented via a Markov chain over finitely many network topologies with independent neighborhoods.