A General Analysis of Sequential Social Learning

Abstract

This paper analyzes a sequential social learning game with a general utility function, state and action space. We show that asymptotic learning holds for every utility function if and only if signals are totally unbounded, i.e., the support of the private posterior probability of every event contains both zero and one. For the case of finitely many actions, we provide a sufficient condition for asymptotic learning depending on the given utility function. Finally, we establish that for the important class of simple utility functions with finitely many actions and states pairwise unbounded signals, which generally is a strictly weaker notion than unbounded signals, are sufficient for asymptotic learning.

Keywords: Social Learning, Information Cascades, Adequate Learning, Asymptotic Learning, Totally Unbounded Signals