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: individuals do at least as well as the most informed agent would do in isolation.
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