Bayesian Learning in Social Networks
Abstract: This work studies 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
We characterize 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 (in particular, as long as the
probability that each individual observes some other from the
recent past converges to one as the social network becomes
large). This result therefore establishes that, with unbounded
private beliefs, there will be asymptotic learning in almost all
reasonable social networks. We also provide rates of learning
for a number of common network topologies.
In contrast, for most network topologies, when private beliefs
are bounded, there will not be asymptotic learning.
Nevertheless, asymptotic learning is possible even with bounded
beliefs in certain stochastic network topologies.
Finally, we characterize equilibria in a generalized environment
with heterogeneity of preferences and show that, contrary to a
naïve intuition, greater diversity (heterogeneity) facilitates
asymptotic learning. For example, with sufficient heterogeneity,
asymptotic learning occurs even when private beliefs are
This is joint work with Munther
Dahleh, Ilan Lobel and Asuman Ozdaglar.
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Daron Acemoglu is Charles P.
Kindleberger Professor of Applied Economics in the Department of
Economics at the Massachusetts Institute of Technology and a
member of the Economic Growth program of the Canadian Institute
of Advanced Research. He is also affiliated with the National
Bureau Economic Research, the Center for Economic Performance,
the Center for Economic Policy Research, and Microsoft Research
Center. He is an elected fellow of the American Academy of Arts
and Sciences, the Econometric Society, the European Economic
Association, and the Society of Labor Economists.
Daron Acemoglu has received a BA in
economics at the University of York, 1989, M.Sc. in mathematical
economics and econometrics at the London School of Economics,
1990, and Ph.D. in economics at the London School of Economics
in 1992. Since 1993, he has held the academic positions of
Lecturer at the London School of Economics, and Assistant
Professor, Pentti Kouri Associate Professor and Professor of
Economics at MIT.
He has received numerous awards and
fellowships, including the award for best paper published in the
Economic Journal in 1996 for his paper "Consumer Confidence and
Rational Expectations: Are Agents' Beliefs Consistent With the
Theory?", the inaugural T. W. Shultz Prize from the University
of Chicago in 2004, and the inaugural Sherwin Rosen Award for
outstanding contribution to labor economics in 2004,
Distinguished Science Award from the Turkish Sciences
Association in 2006, the John von Neumann Award, Rajk College,
Budapest in 2007.
He was also awarded the John Bates
Clark Medal in 2005, given every two years to the best economist
in the United States under the age of 40 by the American
Economic Association, and holds an Honorary Doctorate from the
University of Utrecht.
His work has been published in
leading scholarly journals, including the American Economic
Review, Econometrica, Journal of Political Economy, Quarterly
Journal Economics, Review of Economic Studies, and Mathematics
of Operations Research.
Daron Acemoglu's research covers a
wide range of areas within economics, including political
economy, economic development and growth, human capital theory,
growth theory, innovation, search theory, network economics and
Daron Acemoglu is also the co-editor
of Econometrica and of the National Bureau of Economic Research