Information Heterogeneity and the Speed of Learning in Social Networks

Abstract

This paper examines how the structure of a social network and the quality of information available to different agents determine the speed of social learning. To this end, we study a variant of the seminal model of DeGroot (1974), according to which agents linearly combine their personal experiences with the views of their neighbors. We show that the rate of learning has a simple analytical characterization in terms of the relative entropy of agents’ signal structures and their eigenvector centralities. Our characterization establishes that the way information is dispersed throughout the social network has non-trivial implications for the rate of learning. In particular, we show that when the informativeness of different agents’ signal structures are comparable in the sense of Blackwell (1953), then a positive assortative matching of signal qualities and eigenvector centralities maximizes the rate of learning. On the other hand, if information structures are such that each individual possesses some information crucial for learning, then the rate of learning is higher when agents with the best signals are located at the periphery of the network. Finally, we show that the extent of asymmetry in the structure of the social network plays a key role in the long-run dynamics of the beliefs.

Keywords: Social learning, relative entropy, eigenvector centrality

JEL Classification: D83, D85, Z13