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 (social network).
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 bounded.

This is joint work with Munther Dahleh, Ilan Lobel and Asuman Ozdaglar.

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Biography: 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 learning.

Daron Acemoglu is also the co-editor of Econometrica and of the National Bureau of Economic Research Macroeconomic Annual.


Daron Acemoglu