Granular DeGroot dynamics – a model for robust naive learning in social networks

Amir, Gideon, Arieli, Itai, Ashkenazi-Golan, Galit ORCID: 0000-0003-3896-4131 and Peretz, Ron (2025) Granular DeGroot dynamics – a model for robust naive learning in social networks. Journal of Economic Theory, 223. ISSN 0022-0531

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Abstract

We study a model of opinion exchange in social networks where a state of the world is realized and every agent receives a zero-mean noisy signal of the realized state. Golub and Jackson (2010) have shown that under DeGroot (1974) dynamics agents reach a consensus that is close to the state of the world when the network is large. The DeGroot dynamics, however, is highly non-robust and the presence of a single “adversarial agent” that does not adhere to the updating rule can sway the public consensus to any other value. We introduce a variant of DeGroot dynamics that we call 1/ -DeGroot. 1/ -DeGroot dynamics approximates standard DeGroot dynamics to the nearest rational number with as its denominator and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to standard DeGroot dynamics, 1/ -DeGroot dynamics is highly robust both to the presence of adversarial agents and to certain types of misspecifications.

Item Type:	Article
Additional Information:	© 2024 Elsevier Inc.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics H Social Sciences > HB Economic Theory
JEL classification:	C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C63 - Computational Techniques D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search; Learning; Information and Knowledge; Communication; Belief D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D85 - Network Formation and Analysis: Theory
Date Deposited:	10 Dec 2024 16:09
Last Modified:	09 Jan 2025 11:09
URI:	http://eprints.lse.ac.uk/id/eprint/126309

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