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arXiv · 0807.2028

On Krause's multi-agent consensus model with state-dependent connectivity (Extended version)

Vincent D. Blondel·Julien M. Hendrickx·John N. Tsitsiklis
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Abstract

We study a model of opinion dynamics introduced by Krause: each agent has an opinion represented by a real number, and updates its opinion by averaging all agent opinions that differ from its own by less than 1. We give a new proof of convergence into clusters of agents, with all agents in the same cluster holding the same opinion. We then introduce a particular notion of equilibrium stability and provide lower bounds on the inter-cluster distances at a stable equilibrium. To better understand the behavior of the system when the number of agents is large, we also introduce and study a variant involving a continuum of agents, obtaining partial convergence results and lower bounds on inter-cluster distances, under some mild assumptions.

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Vincent D. Blondel, Julien M. Hendrickx, John N. Tsitsiklis. 2009-03-12. On Krause's multi-agent consensus model with state-dependent connectivity (Extended version). https://arxiv.org/abs/0807.2028

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