Robust Coordination of Linear Threshold Dynamics on Directed Weighted Networks
(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' 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
- Arditti, Laura ; Como, Giacomo LU ; Fagnani, Fabio and Vanelli, Martina
- organization
- publishing date
- 2024
- 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&#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.</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}}, }