Observational learning with position uncertainty

Observational learning is typically examined when agents have precise information about their position in the sequence of play. We present a model in which agents are uncertain about their positions. Agents sample the decisions of past individuals and receive a private signal about the state of the world. We show that social learning is robust to position uncertainty. Under any sampling rule satisfying a stationarity assumption, learning is complete if signal strength is unbounded. In cases with bounded signal strength, we provide a lower bound on information aggregation: individuals do at least as well as an agent with the strongest signal realizations would do in isolation. Finally, we show in a simple environment that position uncertainty slows down learning but not to a great extent.