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

TL;DR

This paper analyzes Krause's opinion dynamics model with state-dependent connectivity, providing new convergence proofs, stability bounds, and extending results to a continuum agent model for large populations.

Contribution

It offers a novel proof of convergence into opinion clusters and introduces a continuum model to study large-scale behavior, with stability and inter-cluster distance bounds.

Findings

Agents form opinion clusters with consensus within each cluster.

Stable equilibria have minimum inter-cluster distances.

Continuum model exhibits partial convergence under mild assumptions.

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.