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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | https://arxiv.org/abs/2409.01593 |
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| _version_ | 1866909303220207616 |
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| author | Chen, Ge Su, Wei Mei, Wenjun Bullo, Francesco |
| author_facet | Chen, Ge Su, Wei Mei, Wenjun Bullo, Francesco |
| contents | The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over $20$ years, its convergence proof is open. Our previous paper \cite{GC-WS-WM-FB:20} solves the problem for the case of uniform weighting factors greater than or equal to $1/2$, but the general case remains unresolved.
This paper considers the DW model with heterogeneous confidence bounds and heterogeneous (unconstrained) weighting factors and shows that, with probability one, the opinion of each agent converges to a fixed vector. In other words, this paper resolves the convergence conjecture for the heterogeneous DW model. Our analysis also clarifies how the convergence speed may be arbitrarily slow under certain parameter conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of the Heterogeneous Deffuant-Weisbuch Model: A Complete Proof and Some Extensions Chen, Ge Su, Wei Mei, Wenjun Bullo, Francesco Optimization and Control Probability The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over $20$ years, its convergence proof is open. Our previous paper \cite{GC-WS-WM-FB:20} solves the problem for the case of uniform weighting factors greater than or equal to $1/2$, but the general case remains unresolved. This paper considers the DW model with heterogeneous confidence bounds and heterogeneous (unconstrained) weighting factors and shows that, with probability one, the opinion of each agent converges to a fixed vector. In other words, this paper resolves the convergence conjecture for the heterogeneous DW model. Our analysis also clarifies how the convergence speed may be arbitrarily slow under certain parameter conditions. |
| title | Convergence of the Heterogeneous Deffuant-Weisbuch Model: A Complete Proof and Some Extensions |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2409.01593 |