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Bayesian Social Learning in a Dynamic Environment

38 Pages Posted: 10 Jan 2018  

Krishna Dasaratha

Harvard University

Benjamin Golub

Harvard University

Nir Hak

Harvard University

Date Written: January 7, 2018

Abstract

Bayesian agents learn about a moving target, such as a commodity price, using private signals and the past estimates of their neighbors in an arbitrary network. The weights they place on these sources of information are endogenously determined by the precisions and correlations of individuals' estimates; these weights, in turn, determine future correlations. We study stationary equilibria—ones in which all of these quantities are constant over time. Equilibria in linear updating rules always exist. This yields a fully Bayesian learning model as tractable as the commonly-used DeGroot heuristic. Equilibria and the comparative statics of learning outcomes can be readily computed even in large networks. Substantively, we identify pervasive inefficiencies in Bayesian learning. In any stationary equilibrium where agents put positive weights on neighbors' actions, learning is Pareto inefficient in a generic network: agents rationally overuse social information and underuse their private signals.

Keywords: social learning, Bayesian learning, DeGroot model, information aggregation, networks, centrality

Suggested Citation

Dasaratha, Krishna and Golub, Benjamin and Hak, Nir, Bayesian Social Learning in a Dynamic Environment (January 7, 2018). Available at SSRN: https://ssrn.com/abstract=3097505

Krishna Dasaratha

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Benjamin Golub (Contact Author)

Harvard University ( email )

Littauer Center, Dept of Economics
1805 Cambridge Street
Cambridge, MA 02138
United States

Nir Hak

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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