Multi-dimensional Hegselmann-Krause dynamics

We consider multi-dimensional Hegselmann-Krause model for opinion dynamics in discrete-time for a set of homogeneous agents. Using dynamic system point of view, we investigate stability properties of the dynamics and show its finite time convergence. The novelty of this work lies in the use of dynamic system approach and the development of Lyapunov-type tools for the analysis of the Hegselmann-Krause model. Furthermore, some new insights and results are provided. The results are valid for any norm that is used to define the neighbor sets.

[1]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[2]  Jan Lorenz,et al.  A stabilization theorem for dynamics of continuous opinions , 2005, 0708.2981.

[3]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[4]  Jan Lorenz,et al.  Repeated Averaging and Bounded Confidence Modeling, Analysis and Simulation of Continuous Opinion Dynamics (Wiederholtes Mitteln bei beschränktem VertrauenModellierung, Analyse und Simulation von kontinuierlicher Meinungsdynamik) , 2007 .

[5]  John N. Tsitsiklis,et al.  On Krause's Multi-Agent Consensus Model With State-Dependent Connectivity , 2008, IEEE Transactions on Automatic Control.

[6]  John N. Tsitsiklis,et al.  Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications , 2009, SIAM J. Control. Optim..

[7]  Behrouz Touri,et al.  On existence of a quadratic comparison function for random weighted averaging dynamics and its implications , 2011, IEEE Conference on Decision and Control and European Control Conference.

[8]  B. Touri.  Hegselmann-Krause Dynamics : An Upper Bound on Termination Time , 2012 .

[9]  B. Touri.  Product of Random Stochastic Matrices and Distributed Averaging , 2012 .

[10]  Tamer Basar,et al.  On averaging dynamics in general state spaces , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).