Opinion dynamics for agents with opinion-dependent connections
(2010) 49th IEEE Conference on Decision and Control (CDC 2010) — Location: Atlanta, Georgia, USA
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- Abstract
- We study a simple continuous-time multi-agent system related to Krause’s model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an intensity proportional to the difference. We prove convergence to a set of clusters, with the agents in each cluster sharing a common value, and provide a lower bound on the distance between clusters at a stable equilibrium, under a suitable notion of multi-agent system stability. To better understand the behavior of the system for a large number of agents, we introduce a variant involving a continuum of agents. We show, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a non-trivial lower bound on the distance between clusters. Finally, we establish that the continuum model accurately represents the asymptotic behavior of a system with a finite but large number of agents.
- Affiliations
Massachusetts Institute of Technology LIDS
Citations
Blondel, V., Hendrickx, J., & Tsitsiklis, J. (2010). Opinion dynamics for agents with opinion-dependent connections. Proceedings of the 49th IEEE Conference on Decision and Control (CDC 2010), 6626-6632. https://doi.org/10.1109/CDC.2010.5717828