Convergence rate of the modified DeGroot-Friedkin model with doubly stochastic relative interaction matrices

Weiguo Xia; Ji Liu; Karl H. Johansson; Tamer Başar

doi:10.1109/ACC.2016.7525054

Convergence rate of the modified DeGroot-Friedkin model with doubly stochastic relative interaction matrices

Weiguo Xia
, Ji Liu
, Karl H. Johansson
, Tamer Başar

Electrical Engineering

Dalian University of Technology
KTH Royal Institute of Technology
University of Illinois at Urbana-Champaign

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

In a recent paper [1], a modified DeGroot-Friedkin model was proposed to study the evolution of the social-confidence levels of individuals in a reflected appraisal mechanism in which a network of n individuals consecutively discuss a sequence of issues. The individuals update their self-confidence levels on one issue in finite time steps, via communicating with their neighbors, instead of waiting until the discussion on the previous issue reaches a consensus, while the neighbor relationships are described by a static relative interaction matrix. This paper studies the same modified DeGroot-Friedkin model, but with time-varying interactions which are characterized by a sequence of doubly stochastic matrices. It is shown that, under appropriate assumptions, the n individuals' self-confidence levels will all converge to 1/n exponentially fast. An explicit expression of the convergence rate is provided.

Original language	English
Title of host publication	2016 American Control Conference, ACC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1054-1059
Number of pages	6
ISBN (Electronic)	9781467386821
DOIs	https://doi.org/10.1109/ACC.2016.7525054
State	Published - Jul 28 2016
Event	2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016

Publication series

Name	Proceedings of the American Control Conference
Volume	2016-July
ISSN (Print)	0743-1619

Conference

Conference	2016 American Control Conference, ACC 2016
Country/Territory	United States
City	Boston
Period	07/6/16 → 07/8/16

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10.1109/ACC.2016.7525054

Cite this

Xia, W., Liu, J., Johansson, K. H., & Başar, T. (2016). Convergence rate of the modified DeGroot-Friedkin model with doubly stochastic relative interaction matrices. In 2016 American Control Conference, ACC 2016 (pp. 1054-1059). Article 7525054 (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525054

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title = "Convergence rate of the modified DeGroot-Friedkin model with doubly stochastic relative interaction matrices",

abstract = "In a recent paper [1], a modified DeGroot-Friedkin model was proposed to study the evolution of the social-confidence levels of individuals in a reflected appraisal mechanism in which a network of n individuals consecutively discuss a sequence of issues. The individuals update their self-confidence levels on one issue in finite time steps, via communicating with their neighbors, instead of waiting until the discussion on the previous issue reaches a consensus, while the neighbor relationships are described by a static relative interaction matrix. This paper studies the same modified DeGroot-Friedkin model, but with time-varying interactions which are characterized by a sequence of doubly stochastic matrices. It is shown that, under appropriate assumptions, the n individuals' self-confidence levels will all converge to 1/n exponentially fast. An explicit expression of the convergence rate is provided.",

author = "Weiguo Xia and Ji Liu and Johansson, \{Karl H.\} and Tamer Ba{\c s}ar",

note = "Publisher Copyright: {\textcopyright} 2016 American Automatic Control Council (AACC).; 2016 American Control Conference, ACC 2016 ; Conference date: 06-07-2016 Through 08-07-2016",

year = "2016",

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doi = "10.1109/ACC.2016.7525054",

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Xia, W, Liu, J, Johansson, KH & Başar, T 2016, Convergence rate of the modified DeGroot-Friedkin model with doubly stochastic relative interaction matrices. in 2016 American Control Conference, ACC 2016., 7525054, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 1054-1059, 2016 American Control Conference, ACC 2016, Boston, United States, 07/6/16. https://doi.org/10.1109/ACC.2016.7525054

Convergence rate of the modified DeGroot-Friedkin model with doubly stochastic relative interaction matrices. / Xia, Weiguo; Liu, Ji; Johansson, Karl H. et al.
2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 1054-1059 7525054 (Proceedings of the American Control Conference; Vol. 2016-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In a recent paper [1], a modified DeGroot-Friedkin model was proposed to study the evolution of the social-confidence levels of individuals in a reflected appraisal mechanism in which a network of n individuals consecutively discuss a sequence of issues. The individuals update their self-confidence levels on one issue in finite time steps, via communicating with their neighbors, instead of waiting until the discussion on the previous issue reaches a consensus, while the neighbor relationships are described by a static relative interaction matrix. This paper studies the same modified DeGroot-Friedkin model, but with time-varying interactions which are characterized by a sequence of doubly stochastic matrices. It is shown that, under appropriate assumptions, the n individuals' self-confidence levels will all converge to 1/n exponentially fast. An explicit expression of the convergence rate is provided.

AB - In a recent paper [1], a modified DeGroot-Friedkin model was proposed to study the evolution of the social-confidence levels of individuals in a reflected appraisal mechanism in which a network of n individuals consecutively discuss a sequence of issues. The individuals update their self-confidence levels on one issue in finite time steps, via communicating with their neighbors, instead of waiting until the discussion on the previous issue reaches a consensus, while the neighbor relationships are described by a static relative interaction matrix. This paper studies the same modified DeGroot-Friedkin model, but with time-varying interactions which are characterized by a sequence of doubly stochastic matrices. It is shown that, under appropriate assumptions, the n individuals' self-confidence levels will all converge to 1/n exponentially fast. An explicit expression of the convergence rate is provided.

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Convergence rate of the modified DeGroot-Friedkin model with doubly stochastic relative interaction matrices

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