This paper provides a formal characterization of the process of rational learning in social networks. Agents receive initial private information and select an action out of a choice set under uncertainty in each of infinitely many periods, observing the history of choices of their neighbors. Choices are made based on a common behavioral rule. Conditions under which rational learning leads to global consensus, local indifference and local disagreement are characterized. In the general setting considered, rational learning can lead to pairs of neighbors selecting different actions once learning ends, while not being indifferent among their choices. The effect of the network structure on the degree of information aggregation and speed of convergence is also considered and an answer to the question of optimal information aggregation in networks provided. The results highlight distinguishing features between properties of Bayesian and non-Bayesian learning in social networks.
Learning social networks common knowledge consensus speed of convergence optimal information aggregation