Journal Article

Bayesian Learning in Social Networks

Daron Acemoglu, Munther A. Dahleh, Ilan Lobel and Asuman Ozdaglar

in The Review of Economic Studies

Published on behalf of Review of Economic Studies Ltd

Volume 78, issue 4, pages 1201-1236
Published in print October 2011 | ISSN: 0034-6527
Published online March 2011 | e-ISSN: 1467-937X | DOI: http://dx.doi.org/10.1093/restud/rdr004
Bayesian Learning in Social Networks

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  • Game Theory and Bargaining Theory
  • Information, Knowledge, and Uncertainy

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We study the (perfect Bayesian) equilibrium of a sequential learning model over a general social network. Each individual receives a signal about the underlying state of the world, observes the past actions of a stochastically generated neighbourhood of individuals, and chooses one of two possible actions. The stochastic process generating the neighbourhoods defines the network topology. We characterize pure strategy equilibria for arbitrary stochastic and deterministic social networks and characterize the conditions under which there will be asymptotic learning—convergence (in probability) to the right action as the social network becomes large. We show that when private beliefs are unbounded (meaning that the implied likelihood ratios are unbounded), there will be asymptotic learning as long as there is some minimal amount of “expansion in observations”. We also characterize conditions under which there will be asymptotic learning when private beliefs are bounded.

Keywords: Information aggregation; Learning; Social networks; Herding; Information cascades; C72; D83

Journal Article.  15060 words.  Illustrated.

Subjects: Game Theory and Bargaining Theory ; Information, Knowledge, and Uncertainy

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