Natural algorithms and influence systems
Communications of the ACM
On the convergence of the Hegselmann-Krause system
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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Influence systems form a large class of multiagent systems designed to model how influence, broadly defined, spreads across a dynamic network. We build a general analytical framework which we then use to prove that, while Turing-complete, influence dynamics of the diffusive type is almost surely asymptotically periodic. Besides resolving the dynamics of a popular family of multiagent systems, the other contribution of this work is to introduce a new type of renormalization-based bifurcation analysis for multiagent systems.