Social Learning through Action-Signals

This paper studies sequential social learning when people learn about others' actions through coarse signals. Agents arrive in cohorts sequentially. Each agent chooses an action upon observing a private "state-signal'' about a payoff-relevant state of the world and "action-signals'' that summarize previous cohorts' actions. I specify conditions under which adequate learning occurs, i.e., agents eventually learn the truth and take the correct actions. A necessary condition for adequate learning is that the state-signals can induce unbounded private likelihoods. When private likelihoods are unbounded, adequate learning occurs if and only if the information environment is "separable". Separability is satisfied under any monotone partitional action-signals