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Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects
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Düring, Bertram, Torregrossa, Marco and Wolfram, Marie-Therese (2019) Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects. Journal of Nonlinear Science, 29 . pp. 1095-1128. doi:10.1007/s00332-018-9512-8 ISSN 0938-8974.
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Official URL: https://doi.org/10.1007/s00332-018-9512-8
Abstract
We propose a mathematical model for opinion formation in a society which is built of two groups, one group of 'ordinary' people and one group of 'strong opinion leaders'. Our approach is based on an opinion formation model introduced in Toscani (2006) and borrows ideas from the kinetic theory of mixtures of rarefied gases. Starting from microscopic interactions among individuals, we arrive at a macroscopic description of the opinion formation process which is characterized by a system of Fokker-Planck type equations. We discuss the steady states of this system, extend it to incorporate emergence and decline of opinion leaders, and present numerical results.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Soccer players -- Rating of -- Mathematical models, Fédération internationale de football association, Fokker-Planck equation | ||||||||||||
Journal or Publication Title: | Journal of Nonlinear Science | ||||||||||||
Publisher: | Springer | ||||||||||||
ISSN: | 0938-8974 | ||||||||||||
Official Date: | 15 June 2019 | ||||||||||||
Dates: |
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Volume: | 29 | ||||||||||||
Page Range: | pp. 1095-1128 | ||||||||||||
DOI: | 10.1007/s00332-018-9512-8 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Journal of Nonlinear Science. The final authenticated version is available online at: https://doi.org/10.1007/s00332-018-9512-8 | ||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
Date of first compliant deposit: | 5 November 2018 | ||||||||||||
Date of first compliant Open Access: | 17 December 2018 | ||||||||||||
RIOXX Funder/Project Grant: |
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