Ulric B. and Evelyn L. Bray Social Sciences Seminar
Abstract: 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. Equilibrium learning may be slow when agents do not observe all predecessors, 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 some members of the previous generation. When this network is sufficiently symmetric, we derive the exact long-run rate of learning as a function of the network parameters. The additional information aggregated by each generation is asymptotically equivalent to fewer than two independent signals, even when generations are arbitrarily large. When agents observe all predecessors from the previous generation, social learning aggregates no more than three signals per generation starting from the third generation, and the long-run learning rate is lower when generations are larger.
Written with Krishna Dasarathaly .