Bauso, D. orcid.org/0000-0001-9713-677X, Tembine, H. and Başar, T. (2016) Opinion Dynamics in Social Networks through Mean-Field Games. SIAM Journal on Control and Optimization, 54 (6). pp. 3225-3257. ISSN 0363-0129
Abstract
Emulation, mimicry, and herding behaviors are phenomena that are observed when multiple social groups interact. To study such phenomena, we consider in this paper a large population of homogeneous social networks. Each such network is characterized by a vector state, a vector-valued controlled input and a vector-valued exogenous disturbance. The controlled input of each network is to align its state to the mean distribution of other networks’ states in spite of the actions of the disturbance. One of the contributions of this paper is a detailed analysis of the resulting mean field game for the cases of both polytopic and L2 bounds on controls and disturbances. A second contribution is the establishment of a robust mean-field equilibrium, that is, a solution including the worst-case value function, the state feedback best-responses for the controlled inputs and worst-case disturbances, and a density evolution. This solution is characterized by the property that no player can benefit from a unilateral deviation even in the presence of the disturbance. As a third contribution, microscopic and macroscopic analyses are carried out to show convergence properties of the population distribution using stochastic stability theory.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Society for Industrial and Applied Mathematics . This is an author produced version of a paper subsequently published in SIAM Journal on Control and Optimization. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Opinion dynamics; mean field games; stochastic stability |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Feb 2017 11:39 |
Last Modified: | 28 Mar 2018 07:41 |
Published Version: | https://doi.org/10.1137/140985676 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Refereed: | Yes |
Identification Number: | 10.1137/140985676 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111488 |