Open Access
August 2011 Scaling limits for continuous opinion dynamics systems
Giacomo Como, Fabio Fagnani
Ann. Appl. Probab. 21(4): 1537-1567 (August 2011). DOI: 10.1214/10-AAP739

Abstract

Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary differential equation describing the system’s mean-field dynamics. Properties of the associated initial value problem are studied. The asymptotic behavior of the solution is analyzed for bounded-confidence opinion dynamics, and in the presence of an heterogeneous influential environment.

Citation

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Giacomo Como. Fabio Fagnani. "Scaling limits for continuous opinion dynamics systems." Ann. Appl. Probab. 21 (4) 1537 - 1567, August 2011. https://doi.org/10.1214/10-AAP739

Information

Published: August 2011
First available in Project Euclid: 8 August 2011

zbMATH: 1235.60136
MathSciNet: MR2857456
Digital Object Identifier: 10.1214/10-AAP739

Subjects:
Primary: 60K35 , 91D30 , 93A15

Keywords: bounded confidence , Multi-agent systems , opinion dynamics , probability-measure-valued ODEs , scaling limits , social networks

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.21 • No. 4 • August 2011
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