Speed of Rational Social Learning in Networks with Gaussian Information

We consider a sequential social-learning environment with rational agents and Gaussian private signals, focusing on how the observation network affects the speed of learning. Agents learn about a binary state and take turns choosing actions based on own signals and network neighbors' behavior. The observation network generally presents an obstruction to the efficient rate of signal aggregation, as agents compromise between incorporating the signals of the observed neighbors and not over-counting the confounding signals of the unobserved early movers. We show that on any network, equilibrium actions are a log-linear function of observations and each agent's accuracy admits a signal-counting interpretation. Adding links to the observation network can harm agents even without introducing new confounds. We then consider a network structure where agents move in generations and observe all members of the previous generation. The additional information aggregated by each generation is asymptotically equivalent to fewer than two independent signals, even when generations are arbitrarily large.