Scaling limits for continuous opinion dynamics systems
Name
Como-2009-Scaling limits for continuous opinion dynamics systems.pdf
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165.52 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Como, Giacomo
Fagnani, Fabio
Date Issued
October 2009
Journal
Proceedings of the 47th Annual Allerton Conference on Communication, Control, and Computing, 2009
Publisher
Institute of Electrical and Electronics Engineers
Citation
Como, Giacomo, and Fagnani, Fabio (2010). Scaling limits for continuous opinion dynamics systems. 47th Annual Allerton Conference on Communication, Control, and Computing, 2009 (Piscataway, N.J.: IEEE): 1562-1566. © 2010 IEEE
Version
Final published version
Abstract
A class of large-scale stochastic discrete-time continuous-opinion dynamical systems is analyzed. Agents have pairwise random interactions in which their vector-valued opinions are updated to a weighted average of their current values. The intensity of the interactions is allowed to depend on the agents' opinions themselves through an interaction kernel. This class of models includes as a special case the bounded-confidence opinion dynamics models recently introduced by Deffuant et al., in which agents interact only when their opinions differ by less than a given threshold, as well as more general interaction kernels. It is shown that, in the limit as the population size increases, upon a proper rescaling of the time index, the trajectories of such stochastic processes concentrate, at an exponential rate, around the solution of a measure-valued differential equation. The asymptotic properties of the solution of such a differential equation are then studied, and convergence is proven to a convex combination of delta measures whose number depends on the interaction kernel.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1109/ALLERTON.2009.5394488
