Lower Bounds on the Rate of Learning in Social Networks
Name
Lobel-2009-Lower Bounds on the Rate of Learning in Social Networks.pdf
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Author(s)
Lobel, Inna
Ozdaglar, Asuman E
Acemoglu, K. Daron
Dahleh, Munther A
Date Issued
July 2009
Journal
American Control Conference, 2009. ACC '09
Publisher
Institute of Electrical and Electronics Engineers
Citation
Lobel, I. et al. “Lower bounds on the rate of learning in social networks.” American Control Conference, 2009. ACC '09. 2009. 2825-2830. ©2009 IEEE.
Version
Final published version
Abstract
e study the rate of convergence of Bayesian learning in social networks. Each individual receives a signal about the underlying state of the world, observes a subset of past actions and chooses one of two possible actions. Our previous work established that when signals generate unbounded likelihood ratios, there will be asymptotic learning under mild conditions on the social network topology-in the sense that beliefs and decisions converge (in probability) to the correct beliefs and action. The question of the speed of learning has not been investigated, however. In this paper, we provide estimates of the speed of learning (the rate at which the probability of the incorrect action converges to zero). We focus on a special class of topologies in which individuals observe either a random action from the past or the most recent action. We show that convergence to the correct action is faster than a polynomial rate when individuals observe the most recent action and is at a logarithmic rate when they sample a random action from the past. This suggests that communication in social networks that lead to repeated sampling of the same individuals lead to slower aggregation of information.
MIT Department
Massachusetts Institute of Technology. Department of Economics
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Operations Research Center
Program in Media Arts and Sciences (Massachusetts Institute of Technology)
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1109/ACC.2009.5160660
