TY - JOUR
AU - Acemoglu, Daron
AU - Dahleh, Munther A
AU - Lobel, Ilan
AU - Ozdaglar, Asuman
TI - Bayesian Learning in Social Networks
JF - National Bureau of Economic Research Working Paper Series
VL - No. 14040
PY - 2008
Y2 - May 2008
DO - 10.3386/w14040
UR - http://www.nber.org/papers/w14040
L1 - http://www.nber.org/papers/w14040.pdf
N1 - Author contact info:
Daron Acemoglu
Department of Economics
MIT
50 Memorial Drive
Cambridge, MA 02142-1347
Tel: 617/253-1927
Fax: 617/253-1330
E-Mail: daron@mit.edu
Munther A. Dahleh
Dept. of Electrical Engineering
and Computer Science
Massachusetts Institute of Technology
77 Massachusetts Ave, 32D-734
Cambridge, MA 02139
E-Mail: dahleh@mit.edu
Ilan Lobel
Stern School of Business
New York University
44 West 4 th St, KMC 8 - 71
New York, NY 10012
Tel: (212) 998 - 0846
E-Mail: ilobel@stern.nyu.edu
Asuman Ozdaglar
Dept of Electrical Engineering
and Computer Science
Massachusetts Institute of Technology
77 Massachusetts Ave, E40-130
Cambridge, MA 02139
E-Mail: asuman@mit.edu
AB - 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 sufficient to ensure asymptotic learning. This theorem therefore establishes that, with unbounded private beliefs, there will be asymptotic learning an 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.
ER -