CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS

• Main Authors: Blondel, Vincent D. (Author), Hendrickx, Julien (Author), Tsitsiklis, John N. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Laboratory for Information and Decision Systems (Contributor)
• Format: Article
• Language: English
• Published: Society for Industrial and Applied Mathematics, 2011-07-08T17:43:44Z.
• Subjects: Article
• Online Access: Get fulltext

 We study a simple continuous-time multiagent 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 multiagent 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 prove, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a nontrivial 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.