Social learning through coarse signals of others' actions

This paper studies a sequential social learning model in which agents learn about an underlying state from others' actions. Unlike classic models, we consider a setting where agents may observe coarse signals of past actions. We identify a simple, necessary, and sufficient condition for asymptotic learning, called separability, which depends on both the information environment and the payoff structure. A necessary condition for separability is “unbounded beliefs” which requires agents' private information to generate strong evidence of the true state, even if only with small probabilities. We also identify conditions on the information environment alone that guarantee separability for all payoff structures. These conditions include unbounded beliefs and a new condition on agents' signals of others' actions, termed double thresholds. Without double thresholds, learning can be confounded so that agents always choose different actions with positive probabilities and never reach a consensus.