Bayesian Learning in Social Networks

53 Pages Posted: 1 Jun 2009

See all articles by Ilan Lobel

Ilan Lobel

Massachusetts Institute of Technology (MIT) - Operations Research Center

Munther Dahleh

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science

Daron Acemoglu

Massachusetts Institute of Technology (MIT) - Department of Economics; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Asuman E. Ozdaglar

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science

Multiple version iconThere are 2 versions of this paper

Date Written: May 11, 2008

Abstract

We study the (perfect Bayesian) equilibrium of a model of learning 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 neighborhood of individuals, and chooses one of two possible actions. The stochastic process generating the neighborhoods defines the network topology (social network). The special case where each individual observes all past actions has been widely studied in the literature. We characterize pure-strategy equilibria for arbitrary stochastic and deterministic social networks and characterize the conditions under which there will be asymptotic learning|that is, the conditions under which, as the social network becomes large, individuals converge (in probability) to taking the right action. 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. Our main theorem shows that when the probability that each individual observes some other individual from the recent past converges to one as the social network becomes large, unbounded private beliefs are su±cient to ensure asymptotic learning. This theorem therefore establishes that, with unbounded private beliefs, there will be asymptotic learning in almost all reasonable social networks. We also show that for most network topologies, when private beliefs are bounded, there will not be asymptotic learning. In addition, in contrast to the special case where all past actions are observed, asymptotic learning is possible even with bounded beliefs in certain stochastic network topologies.

Keywords: information aggregation, learning, social networks, herding, information cascades

Suggested Citation

Lobel, Ilan and Dahleh, Munther and Acemoglu, Daron and Ozdaglar, Asuman E., Bayesian Learning in Social Networks (May 11, 2008). NYU, Stern, Center for Digital Economy Research, Vol. , pp. -, 2009. Available at SSRN: https://ssrn.com/abstract=1399883

Ilan Lobel (Contact Author)

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

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Munther Dahleh

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science ( email )

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Daron Acemoglu

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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Centre for Economic Policy Research (CEPR)

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National Bureau of Economic Research (NBER)

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Asuman E. Ozdaglar

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science ( email )

50 Memorial Drive
Cambridge, MA 02139-4307
United States
617-324-0058 (Phone)

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