On Krause's Multi-Agent Consensus Model With State-Dependent Connectivity

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 one. We give a new proof of convergence into clusters of agents, with all agents in the sam...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2009-11, Vol.54 (11), p.2586-2597
Main Authors: Blondel, V.D., Hendrickx, J.M., Tsitsiklis, J.N.
Format: Article
Language:English
Subjects:
Animals
Applied sciences
Artificial intelligence
Automatic control
Clusters
Computer science
control theory
systems
Computer systems and distributed systems. User interface
Consensus
Continuums
Convergence
decentralized control
Decision theory. Utility theory
Distributed control
Dynamic tests
Dynamics
Educational programs
Exact sciences and technology
Laboratories
Lower bounds
multi-agent system
Multiagent systems
Operational research and scientific management
Operational research. Management science
opinion dynamics
Software
Stability
Topology
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Summary: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 one. 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2009.2031211