IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v60y2010i1p69-78.html
   My bibliography  Save this article

Trust, influence, and convergence of behavior in social networks

Author

Listed:
  • Pan, Zhengzheng

Abstract

I propose a social learning framework where agents repeatedly take the weighted average of all agents' current opinions in forming their own for the next period. They also update the influence weights that they place on each other. It is proven that both opinions and the influence weights are convergent. In the steady state, opinions reach consensus and influence weights are distributed evenly. Convergence occurs with an extended model as well, which indicates the tremendous influential power possessed by a minority group. Computer simulations of the updating processes provide supportive evidence.

Suggested Citation

  • Pan, Zhengzheng, 2010. "Trust, influence, and convergence of behavior in social networks," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 69-78, July.
    • Handle: RePEc:eee:matsoc:v:60:y:2010:i:1:p:69-78
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(10)00026-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stephen Leider & Markus M. Möbius & Tanya Rosenblat & Quoc-Anh Do, 2009. "Directed Altruism and Enforced Reciprocity in Social Networks," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(4), pages 1815-1851.
    2. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
    3. Matthew O. Jackson & Benjamin Golub, 2007. "Naïve Learning in Social Networks: Convergence, Influence and Wisdom of Crowds," Working Papers 2007.64, Fondazione Eni Enrico Mattei.
    4. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    5. Durieu, Jacques & Solal, Philippe, 2003. "Adaptive play with spatial sampling," Games and Economic Behavior, Elsevier, vol. 43(2), pages 189-195, May.
    6. Lorenz, Jan, 2005. "A stabilization theorem for dynamics of continuous opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 217-223.
    7. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 93-125.
    8. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
    9. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-643, August.
    10. Shiller, Robert J, 1995. "Conversation, Information, and Herd Behavior," American Economic Review, American Economic Association, vol. 85(2), pages 181-185, May.
    11. Vernette, ÉRic, 2004. "Targeting Women's Clothing Fashion Opinion Leaders in Media Planning: An Application for Magazines," Journal of Advertising Research, Cambridge University Press, vol. 44(1), pages 90-107, March.
    12. Duncan J. Watts & Peter Sheridan Dodds, 2007. "Influentials, Networks, and Public Opinion Formation," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 34(4), pages 441-458, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    2. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    3. Polanski, Arnold & Vega-Redondo, Fernando, 2023. "Homophily and influence," Journal of Economic Theory, Elsevier, vol. 207(C).
    4. Diamantaras, Dimitrios & Gilles, Robert P., 2011. "Ambiguity, social opinion and the use of common property resources," Journal of Economic Behavior & Organization, Elsevier, vol. 80(1), pages 210-222.
    5. Zhengzheng Pan, 2012. "Opinions and Networks: How Do They Effect Each Other," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 157-171, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    2. Daron Acemoglu & Asuman Ozdaglar, 2011. "Opinion Dynamics and Learning in Social Networks," Dynamic Games and Applications, Springer, vol. 1(1), pages 3-49, March.
    3. Daron Acemoglu & Munther A. Dahleh & Ilan Lobel & Asuman Ozdaglar, 2011. "Bayesian Learning in Social Networks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1201-1236.
    4. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    5. Michel Grabisch & Agnieszka Rusinowska, 2020. "A Survey on Nonstrategic Models of Opinion Dynamics," Games, MDPI, vol. 11(4), pages 1-29, December.
    6. Akylai Taalaibekova, 2018. "Opinion formation in social networks," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 85-108.
    7. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining models of influence," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(2), pages 69-85.
    8. Rusinowska, Agnieszka & Taalaibekova, Akylai, 2019. "Opinion formation and targeting when persuaders have extreme and centrist opinions," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 9-27.
    9. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    10. Jadbabaie, Ali & Molavi, Pooya & Sandroni, Alvaro & Tahbaz-Salehi, Alireza, 2012. "Non-Bayesian social learning," Games and Economic Behavior, Elsevier, vol. 76(1), pages 210-225.
    11. Michel Grabisch & Agnieszka Rusinowska, 2016. "Determining influential models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01318081, HAL.
    12. Isabel Melguizo, 2019. "Homophily and the Persistence of Disagreement," The Economic Journal, Royal Economic Society, vol. 129(619), pages 1400-1424.
    13. Michel Grabisch & Agnieszka Rusinowska, 2010. "Iterating influence between players in a social network," Documents de travail du Centre d'Economie de la Sorbonne 10089, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. Azzimonti, Marina & Fernandes, Marcos, 2023. "Social media networks, fake news, and polarization," European Journal of Political Economy, Elsevier, vol. 76(C).
    15. Matthew O. Jackson & Benjamin Golub, 2007. "Naïve Learning in Social Networks: Convergence, Influence and Wisdom of Crowds," Working Papers 2007.64, Fondazione Eni Enrico Mattei.
    16. Camargo, Braz, 2014. "Learning in society," Games and Economic Behavior, Elsevier, vol. 87(C), pages 381-396.
    17. Matjaž Steinbacher & Mitja Steinbacher, 2019. "Opinion Formation with Imperfect Agents as an Evolutionary Process," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 479-505, February.
    18. Lilian Ng & Fei Wu, 2010. "Peer Effects in the Trading Decisions of Individual Investors," Financial Management, Financial Management Association International, vol. 39(2), pages 807-831, June.
    19. Tsakas, Nikolas, 2012. "Naive learning in social networks: Imitating the most successful neighbor," MPRA Paper 37796, University Library of Munich, Germany.
    20. Li-Xin Wang, 2016. "Modeling Stock Price Dynamics with Fuzzy Opinion Networks," Papers 1602.06213, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:60:y:2010:i:1:p:69-78. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.