Joint Colloquium Distinguished Lecture Series

Bayesian Learning in Social Networks

Ilan Lobel Wednesday, March 11, 2009
306 Soda Hall (HP Auditorium)
4:00 - 5:00 pm

Ilan Lobel
Grad Student, Massachusetts Institute of Technology (MIT)

Abstract:

We study the (perfect Bayesian) equilibrium of a dynamic game where each agent receives a signal about an 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. 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. Joint work with Daron Acemoglu, Munther Dahleh and Asu Ozdaglar.

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