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

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 opini ons 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 s ame 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 bet ter understand the behavior of the system when the number of agents is large, we also introduce and study a variant involv ing a continuum of agents, obtaining partial convergence resul ts and lower bounds on inter-cluster distances, under some mil d assumptions.

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