CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS
We study a simple continuous-time multiagent 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 convergenc...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2011
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| Online Access: | http://hdl.handle.net/1721.1/64777 https://orcid.org/0000-0003-2658-8239 |
| _version_ | 1826208156232974336 |
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| author | Blondel, Vincent D. Hendrickx, Julien Tsitsiklis, John N. |
| 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 Blondel, Vincent D. Hendrickx, Julien Tsitsiklis, John N. |
| author_sort | Blondel, Vincent D. |
| collection | MIT |
| description | We study a simple continuous-time multiagent 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 multiagent 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 prove, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a nontrivial 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 | 2024-09-23T14:01:24Z |
| format | Article |
| id | mit-1721.1/64777 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:01:24Z |
| publishDate | 2011 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/647772022-10-01T18:38:13Z CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS Blondel, Vincent D. Hendrickx, Julien Tsitsiklis, John N. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Tsitsiklis, John N. Tsitsiklis, John N. We study a simple continuous-time multiagent 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 multiagent 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 prove, under some conditions, the existence of a solution to the system dynamics, convergence to clusters, and a nontrivial 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 ECCS-0701623) 2011-07-08T17:43:44Z 2011-07-08T17:43:44Z 2010-10 2009-07 Article http://purl.org/eprint/type/JournalArticle 0363-0129 1095-7138 http://hdl.handle.net/1721.1/64777 Blondel, Vincent D., Julien M. Hendrickx, and John N. Tsitsiklis. “Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications.” SIAM Journal on Control and Optimization 48.8 (2010) : 5214. © 2010 Society for Industrial and Applied Mathematics https://orcid.org/0000-0003-2658-8239 en_US http://dx.doi.org/10.1137/090766188 SIAM Journal on Control and Optimization 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 Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | Blondel, Vincent D. Hendrickx, Julien Tsitsiklis, John N. CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS |
| title | CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS |
| title_full | CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS |
| title_fullStr | CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS |
| title_full_unstemmed | CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS |
| title_short | CONTINUOUS-TIME AVERAGE-PRESERVING OPINION DYNAMICS WITH OPINION-DEPENDENT COMMUNICATIONS |
| title_sort | continuous time average preserving opinion dynamics with opinion dependent communications |
| url | http://hdl.handle.net/1721.1/64777 https://orcid.org/0000-0003-2658-8239 |
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