Asymptotic learning on Bayesian social networks

Elchanan Mossel; Allan Sly; Omer Tamuz

doi:10.1007/s00440-013-0479-y

Asymptotic learning on Bayesian social networks

Elchanan Mossel, Allan Sly, Omer Tamuz

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

We study a standard model of economic agents on the nodes of a social network graph who learn a binary "state of the world" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs G_n = (V_n,E_n) with {pipe}V_n{pipe} → ∞ if with probability tending to 1 as n → ∞ all agents in G_n eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.

Original language	English (US)
Pages (from-to)	127-157
Number of pages	31
Journal	Probability Theory and Related Fields
Volume	158
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-013-0479-y
State	Published - Feb 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Aggregation of information
Bayesian learning
Rational expectations
Social networks

Access to Document

10.1007/s00440-013-0479-y

Cite this

@article{543acd00748d4cce81b9622098f5d703,

title = "Asymptotic learning on Bayesian social networks",

abstract = "We study a standard model of economic agents on the nodes of a social network graph who learn a binary {"}state of the world{"} S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs Gn = (Vn,En) with \{pipe\}Vn\{pipe\} → ∞ if with probability tending to 1 as n → ∞ all agents in Gn eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.",

keywords = "Aggregation of information, Bayesian learning, Rational expectations, Social networks",

author = "Elchanan Mossel and Allan Sly and Omer Tamuz",

note = "Funding Information: The authors would like to thank Shachar Kariv for an enthusiastic introduction to his work with Douglas Gale, and for suggesting the significance of asymptotic learning in this model. Elchanan Mossel is supported by NSF award DMS 1106999, by ONR award N000141110140 and by ISF Grant 1300/08. Allan Sly is supported in part by an Alfred Sloan Fellowship in Mathematics. Omer Tamuz is supported by ISF Grant 1300/08, and is a recipient of the Google Europe Fellowship in Social Computing. This research is supported in part by this Google Fellowship. ",

year = "2014",

month = feb,

doi = "10.1007/s00440-013-0479-y",

language = "English (US)",

volume = "158",

pages = "127--157",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - Asymptotic learning on Bayesian social networks

AU - Mossel, Elchanan

AU - Sly, Allan

AU - Tamuz, Omer

N1 - Funding Information: The authors would like to thank Shachar Kariv for an enthusiastic introduction to his work with Douglas Gale, and for suggesting the significance of asymptotic learning in this model. Elchanan Mossel is supported by NSF award DMS 1106999, by ONR award N000141110140 and by ISF Grant 1300/08. Allan Sly is supported in part by an Alfred Sloan Fellowship in Mathematics. Omer Tamuz is supported by ISF Grant 1300/08, and is a recipient of the Google Europe Fellowship in Social Computing. This research is supported in part by this Google Fellowship.

PY - 2014/2

Y1 - 2014/2

N2 - We study a standard model of economic agents on the nodes of a social network graph who learn a binary "state of the world" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs Gn = (Vn,En) with {pipe}Vn{pipe} → ∞ if with probability tending to 1 as n → ∞ all agents in Gn eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.

AB - We study a standard model of economic agents on the nodes of a social network graph who learn a binary "state of the world" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs Gn = (Vn,En) with {pipe}Vn{pipe} → ∞ if with probability tending to 1 as n → ∞ all agents in Gn eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.

KW - Aggregation of information

KW - Bayesian learning

KW - Rational expectations

KW - Social networks

UR - https://www.scopus.com/pages/publications/84892870636

UR - https://www.scopus.com/inward/citedby.url?scp=84892870636&partnerID=8YFLogxK

U2 - 10.1007/s00440-013-0479-y

DO - 10.1007/s00440-013-0479-y

M3 - Article

AN - SCOPUS:84892870636

SN - 0178-8051

VL - 158

SP - 127

EP - 157

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -

Asymptotic learning on Bayesian social networks

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this