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http://hdl.handle.net/2451/28065
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| Title: | Bayesian Learning in Social Networks |
| Authors: | Lobel, Ilan
Dahleh, Munther
Acemoglu, Daron
Ozdaglar, Asuman |
| Keywords: | information aggregation
learning
social networks
herding
information cascades |
| Issue Date: | 1-May-2009 |
| Series/Report no.: | CeDER-09-01 |
| Abstract: | We study the (perfect Bayesian) equilibrium of a model of learning over
a general so- cial 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 de¯nes 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, un- bounded
private beliefs are su±cient to ensure asymptotic learning. This
theorem there- fore 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. |
| URI: | http://hdl.handle.net/2451/28065 |
| Appears in Collections: | CeDER Working Papers
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