2013/11/13 by Olle Häggström, Häggström, Olle, Timo Hirscher +1
Decision Sciences · Physics and Astronomy · #60K35 #Complex Network Analysis Techniques #FOS: Mathematics #Game Theory and Applications #Opinion Dynamics and Social Influence #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1311.3223
openalex publication_date 2013/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The so-called Deffuant model describes a pattern for social interaction, in which two neighboring individuals randomly meet and share their opinions on a certain topic, if their discrepancy is not beyond a given threshold θ. The major focus of the analyses, both theoretical and based on simulations, lies on whether these single interactions lead to a global consensus in the long run or not. First, we generalize a result of Lanchier for the Deffuant model on ℤ, determining the critical value for θ at which a phase transition of the long term behavior takes place, to other distributions of the initial opinions than i.i.d. uniform on [0,1]. Then we shed light on the situations where the underlying line graph ℤ is replaced by higher-dimensional lattices ℤd, d≥2, or the infinite cluster of supercritical i.i.d. bond percolation on these lattices.