Bayesian Learning in Social Networks
53 Pages Posted: 1 Jun 2009
There are 2 versions of this paper
Bayesian Learning in Social Networks
Bayesian Learning in Social Networks
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: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
Persuasion Bias, Social Influence, and Uni-Dimensional Opinions
By Peter M. Demarzo, Jeffrey Zwiebel, ...
-
Naive Learning in Social Networks: Convergence, Influence and Wisdom of Crowds
By Matthew O. Jackson and Benjamin Golub
-
Bayesian Learning in Social Networks
By Daron Acemoglu, Munther Dahleh, ...
-
Opinion Dynamics and Learning in Social Networks
By Daron Acemoglu and Asuman E. Ozdaglar
-
Rational Social Learning by Random Sampling
By Lones Smith and Peter Norman Sorensen
-
Information Percolation in Segmented Markets
By Darrell Duffie, Gustavo Manso, ...
-
Information Percolation in Segmented Markets
By Darrell Duffie, Semyon Malamud, ...
-
How Homophily Affects the Speed of Learning and Best Response Dynamics
By Benjamin Golub and Matthew O. Jackson
-
Spread of (Mis)Information in Social Networks
By Daron Acemoglu, Asuman E. Ozdaglar, ...
-
Dynamics of Information Exchange in Endogenous Social Networks
By Daron Acemoglu, Kostas Bimpikis, ...