Observational Learning Under Imperfect Information

We explore Bayes-rational sequential decision making in a game with pure information externalities, where each decision maker observes only her predecessor's binary action. Under perfect information the martingale property of the stochastic learning process is used to establish convergence of beliefs and actions. Under imperfect information, in contrast, beliefs and actions cycle forever. However, despite the stochastic instability, over time the private information is ignored and decision makers become increasingly likely to imitate their predecessors. Consequently, we observe longer and longer periods of uniform behavior, punctuated by increasingly rare switches.