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 are allowed to have arbitrary ex-ante beliefs about their positions: they may observe their position perfectly, imperfectly, or not at all. 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 show that agents achieve what we define as constrained efficient learning: all individuals do at least as well as the most informed agent would do in isolation. JEL Classification: C72, D83, D85 †We are grateful to Bill Sandholm for his advice, suggestions and encouragement. We also thank Dan Quint, Ricardo Serrano-Padial, Marzena Rostek, Marek Weretka, Ben Cowan, Marı́a Eugenia Garibotti, Danqing Hu, Sang Yoon Lee, Fernando Louge and David Rivers for valuable comments. All remaining errors are ours.