Ilan Lobel

Massachusetts Institute of Technology

Wu & Chen Auditorium

11:00 am – 12:00 pm

"Bayesian Learning in Social Networks"

 

Abstract

We study the learning problem of a set of consumers connected via a general social network. Each consumer decides whether to purchase a > product of unknown quality based on their signal and their observation of a subset of past consumer choices. This model approximates both the > problem of learning from the observed actions of friends and neighbors > and behavior resulting from recommendation systems. We focus on whether > consumers will eventually learn the quality of the product.

Formally, 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.

Bio

Ilan Lobel is a Ph.D. candidate in Operations Research at the Massachusetts Institute of Technology. His main research interest is the analysis and design of large-scale multi-agent networked systems that straddle the traditional boundaries of operations research, engineering and economics.