Social Learning in a Dynamic Environment
73 Pages Posted: 10 Jan 2018 Last revised: 3 Aug 2018
Date Written: July 26, 2018
Agents learn about a state using private signals and the past actions of their neighbors. In contrast to most models of social learning in a network, the target being learned about is moving around. We ask: when can a group aggregate information quickly, keeping up with the changing state? First, if private signal distributions are diverse enough across agents, then Bayesian learning achieves good information aggregation as long as individuals observe sufficiently many others. Second, without such diversity, Bayesian information aggregation can fall far short of good aggregation benchmarks, and can be Pareto-inefficient. Third, good aggregation requires anti-imitation; without it, agents' estimates are inefficiently confounded by "echoes." Our stationary equilibrium learning rules incorporate past information by taking linear combinations of other agents' past estimates (as in the simple DeGroot heuristic), and we characterize the coefficients in these linear combinations. The resulting tractability can facilitate structural estimation of equilibrium learning models and testing against behavioral alternatives, as well as the analysis of welfare and influence.
Keywords: social learning, Bayesian learning, DeGroot model, information aggregation, networks, centrality
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