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Robust Coordination of Linear Threshold Dynamics on Directed Weighted Networks

Arditti, Laura ; Como, Giacomo LU ; Fagnani, Fabio and Vanelli, Martina (2024) In IEEE Transactions on Automatic Control
Abstract

We study dynamics in a network of interacting agents updating their binary states according to a time-varying threshold rule. Specifically, agents revise their state asynchronously by comparing the weighted average of the current states of their neighbors in the interaction network with possibly heterogeneous time-varying threshold values. Such thresholds are determined by an exogenous signal representing an external influence field modeling the different agents' biases towards one state with respect to the other one. We prove necessary and sufficient conditions for global stability of consensus equilibria, robustly with respect to the (constant or time-varying) external field. Our results apply to general weighted directed... (More)

We study dynamics in a network of interacting agents updating their binary states according to a time-varying threshold rule. Specifically, agents revise their state asynchronously by comparing the weighted average of the current states of their neighbors in the interaction network with possibly heterogeneous time-varying threshold values. Such thresholds are determined by an exogenous signal representing an external influence field modeling the different agents&#x0027; biases towards one state with respect to the other one. We prove necessary and sufficient conditions for global stability of consensus equilibria, robustly with respect to the (constant or time-varying) external field. Our results apply to general weighted directed interaction networks and build on super-modularity properties of certain network coordination games whose best response dynamics coincide with the linear threshold dynamics. In particular, we introduce a novel notion of <italic>robust improvement paths</italic> for such games and characterize necessary and sufficient conditions for their existence.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Behavioral sciences, best response dynamics, Biological system modeling, coordination games, Europe, Games, Linear threshold dynamics, network games, network robustness, Robust stability, robust stability, Robustness, Vectors
in
IEEE Transactions on Automatic Control
pages
15 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85187026433
ISSN
0018-9286
DOI
10.1109/TAC.2024.3371882
language
English
LU publication?
yes
id
0791ac63-29ed-4402-b0ec-cc01413531a7
date added to LUP
2024-04-02 10:50:23
date last changed
2024-04-02 10:50:57
@article{0791ac63-29ed-4402-b0ec-cc01413531a7,
  abstract     = {{<p>We study dynamics in a network of interacting agents updating their binary states according to a time-varying threshold rule. Specifically, agents revise their state asynchronously by comparing the weighted average of the current states of their neighbors in the interaction network with possibly heterogeneous time-varying threshold values. Such thresholds are determined by an exogenous signal representing an external influence field modeling the different agents&amp;#x0027; biases towards one state with respect to the other one. We prove necessary and sufficient conditions for global stability of consensus equilibria, robustly with respect to the (constant or time-varying) external field. Our results apply to general weighted directed interaction networks and build on super-modularity properties of certain network coordination games whose best response dynamics coincide with the linear threshold dynamics. In particular, we introduce a novel notion of &lt;italic&gt;robust improvement paths&lt;/italic&gt; for such games and characterize necessary and sufficient conditions for their existence.</p>}},
  author       = {{Arditti, Laura and Como, Giacomo and Fagnani, Fabio and Vanelli, Martina}},
  issn         = {{0018-9286}},
  keywords     = {{Behavioral sciences; best response dynamics; Biological system modeling; coordination games; Europe; Games; Linear threshold dynamics; network games; network robustness; Robust stability; robust stability; Robustness; Vectors}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{Robust Coordination of Linear Threshold Dynamics on Directed Weighted Networks}},
  url          = {{http://dx.doi.org/10.1109/TAC.2024.3371882}},
  doi          = {{10.1109/TAC.2024.3371882}},
  year         = {{2024}},
}