Lower Bounds on the Rate of Learning in Social Networks
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...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2010
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| Online Access: | http://hdl.handle.net/1721.1/59971 https://orcid.org/0000-0002-1827-1285 https://orcid.org/0000-0002-1470-2148 https://orcid.org/0000-0003-0908-7491 |
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| author | Lobel, Inna Ozdaglar, Asuman E Acemoglu, K. Daron Dahleh, Munther A |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Lobel, Inna Ozdaglar, Asuman E Acemoglu, K. Daron Dahleh, Munther A |
| author_sort | Lobel, Inna |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:00:50Z |
| format | Article |
| id | mit-1721.1/59971 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:00:50Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/599712022-09-30T18:16:59Z Lower Bounds on the Rate of Learning in Social Networks Lobel, Inna Ozdaglar, Asuman E Acemoglu, K. Daron Dahleh, Munther A 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) Ozdaglar, Asuman E. Ozdaglar, Asuman E. Acemoglu, Daron Lobel, Inna Dahleh, Munther A. 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. 2010-11-12T16:10:45Z 2010-11-12T16:10:45Z 2009-07 2009-06 Article http://purl.org/eprint/type/ConferencePaper Print ISBN: 978-1-4244-4523-3 0743-1619 INSPEC Accession Number: 10776036 http://hdl.handle.net/1721.1/59971 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. https://orcid.org/0000-0002-1827-1285 https://orcid.org/0000-0002-1470-2148 https://orcid.org/0000-0003-0908-7491 en_US http://dx.doi.org/10.1109/ACC.2009.5160660 American Control Conference, 2009. ACC '09 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. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | Lobel, Inna Ozdaglar, Asuman E Acemoglu, K. Daron Dahleh, Munther A Lower Bounds on the Rate of Learning in Social Networks |
| title | Lower Bounds on the Rate of Learning in Social Networks |
| title_full | Lower Bounds on the Rate of Learning in Social Networks |
| title_fullStr | Lower Bounds on the Rate of Learning in Social Networks |
| title_full_unstemmed | Lower Bounds on the Rate of Learning in Social Networks |
| title_short | Lower Bounds on the Rate of Learning in Social Networks |
| title_sort | lower bounds on the rate of learning in social networks |
| url | http://hdl.handle.net/1721.1/59971 https://orcid.org/0000-0002-1827-1285 https://orcid.org/0000-0002-1470-2148 https://orcid.org/0000-0003-0908-7491 |
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