Value of Information in Social Learning

Abstract

This study extends Blackwell's (1953) comparison of information to a sequential social learning model in which agents make decisions sequentially based on both private signals and observed actions of others. In this context, we introduce a binary relation over information structures: an information structure is {\it more socially valuable} than another if it yields higher expected payoffs for {\it all} agents, regardless of their preferences and equilibrium realizations. First, we establish that this binary relation is strictly stronger than the Blackwell order. Next, we provide a necessary and sufficient condition for our binary relation and propose a simpler sufficient condition that is easier to verify. We further explore comparisons of information structures in terms of long-run payoffs, limit welfare, and canonical binary environments.