Opinion dynamics for agents with opinion-dependent connections
We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an intensity proportional to the difference. We prove convergen...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/73145 https://orcid.org/0000-0003-2658-8239 |
| _version_ | 1826207878048907264 |
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| author | Tsitsiklis, John N. Hendrickx, Julien Blondel, Vincent D. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Tsitsiklis, John N. Hendrickx, Julien Blondel, Vincent D. |
| author_sort | Tsitsiklis, John N. |
| collection | MIT |
| description | We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an intensity proportional to the difference. We prove convergence to a set of clusters, with the agents in each cluster sharing a common value, and provide a lower bound on the distance between clusters at a stable equilibrium, under a suitable notion of multi-agent system stability. To better understand the behavior of the system for a large number of agents, we introduce a variant involving a continuum of agents. We show, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a non-trivial lower bound on the distance between clusters. Finally, we establish that the continuum model accurately represents the asymptotic behavior of a system with a finite but large number of agents. |
| first_indexed | 2024-09-23T13:56:22Z |
| format | Article |
| id | mit-1721.1/73145 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:56:22Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/731452022-09-28T17:13:47Z Opinion dynamics for agents with opinion-dependent connections Tsitsiklis, John N. Hendrickx, Julien Blondel, Vincent D. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Tsitsiklis, John N. We study a simple continuous-time multi-agent system related to Krause's model of opinion dynamics: each agent holds a real value, and this value is continuously attracted by every other value differing from it by less than 1, with an intensity proportional to the difference. We prove convergence to a set of clusters, with the agents in each cluster sharing a common value, and provide a lower bound on the distance between clusters at a stable equilibrium, under a suitable notion of multi-agent system stability. To better understand the behavior of the system for a large number of agents, we introduce a variant involving a continuum of agents. We show, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a non-trivial lower bound on the distance between clusters. Finally, we establish that the continuum model accurately represents the asymptotic behavior of a system with a finite but large number of agents. National Science Foundation (U.S.) (grant no. ECCS-0701623) 2012-09-25T12:34:04Z 2012-09-25T12:34:04Z 2011-02 2010-12 Article http://purl.org/eprint/type/ConferencePaper 978-1-4244-7745-6 0743-1546 http://hdl.handle.net/1721.1/73145 Tsitsiklis, John N. et al. "Opinion dynamics for agents with opinion-dependent connections." Proceedings of the 2010 IEEE Conference on Decision and Control (CDC): 6626-6632. © 2010 IEEE. https://orcid.org/0000-0003-2658-8239 en_US http://dx.doi.org/ 10.1109/CDC.2010.5717828 Proceedings of the 49th IEEE Conference on Decision and Control (CDC), 2010 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers (IEEE) IEEE |
| spellingShingle | Tsitsiklis, John N. Hendrickx, Julien Blondel, Vincent D. Opinion dynamics for agents with opinion-dependent connections |
| title | Opinion dynamics for agents with opinion-dependent connections |
| title_full | Opinion dynamics for agents with opinion-dependent connections |
| title_fullStr | Opinion dynamics for agents with opinion-dependent connections |
| title_full_unstemmed | Opinion dynamics for agents with opinion-dependent connections |
| title_short | Opinion dynamics for agents with opinion-dependent connections |
| title_sort | opinion dynamics for agents with opinion dependent connections |
| url | http://hdl.handle.net/1721.1/73145 https://orcid.org/0000-0003-2658-8239 |
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