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

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  • Amir, Gideon
  • Arieli, Itai
  • Ashkenazi-Golan, Galit
  • Peretz, Ron

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 1m-DeGroot. 1m-DeGroot dynamics approximates standard DeGroot dynamics to the nearest rational number with m as its denominator and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to standard DeGroot dynamics, 1m-DeGroot dynamics is highly robust both to the presence of adversarial agents and to certain types of misspecifications.

Suggested Citation

  • Amir, Gideon & Arieli, Itai & Ashkenazi-Golan, Galit & Peretz, Ron, 2025. "Granular DeGroot dynamics – A model for robust naive learning in social networks," Journal of Economic Theory, Elsevier, vol. 223(C).
    • Handle: RePEc:eee:jetheo:v:223:y:2025:i:c:s0022053124001583
    DOI: 10.1016/j.jet.2024.105952
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