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Social learning with bounded confidence and heterogeneous agents

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  • Liu, Qipeng
  • Wang, Xiaofan
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    Abstract

    This paper investigates an opinion formation model in social networks with bounded confidence and heterogeneous agents. The network topologies are shaped by the homophily of beliefs, which means any pair of agents are neighbors only if their belief difference is not larger than a positive constant called the bound of confidence. We consider a model with both informed agents and uninformed agents, the essential difference between which is the informed agents have access to outside signals which are function of the underlying true state of the social event concerned. More precisely, the informed agents update their beliefs by combining the Bayesian posterior beliefs based on their private observations and weighted averages of the beliefs of their neighbors. The uninformed agents update their beliefs simply by linearly combining the beliefs of their neighbors. We find that the whole group can learn the true state only if the bound of confidence is larger than a positive threshold which is related to the population density. Furthermore, simulations show that the proportion of informed agents required for collective learning decreases as the population density increases. By tuning the learning speed of informed agents, we find the following: the higher the speed, the shorter the time needed for the whole group to achieve a steady state, and on the other hand, the higher the speed, the lower the proportion of agents with successful learning — there is a trade-off.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 392 (2013)
    Issue (Month): 10 ()
    Pages: 2368-2374

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    Handle: RePEc:eee:phsmap:v:392:y:2013:i:10:p:2368-2374

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Social networks; Opinion formation; Learning; Bounded confidence; Heterogeneous agents;

    References

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    1. Peter M. Demarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, And Unidimensional Opinions," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 118(3), pages 909-968, August.
    2. 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.
    3. Daron Acemoglu & Asuman E. Ozdaglar, 2010. "Opinion Dynamics and Learning in Social Networks," Levine's Working Paper Archive 661465000000000222, David K. Levine.
    4. Guillaume Deffuant & Frederic Amblard & G�rard Weisbuch, 2002. "How Can Extremism Prevail? a Study Based on the Relative Agreement Interaction Model," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(4), pages 1.
    5. 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.
    6. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
    7. Abhijit Banerjee & Drew Fudenberg, 2010. "Word of Mouth Learning," Levine's Working Paper Archive 723, David K. Levine.
    8. 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 2.
    9. Rabin, Matthew, 1997. "Psychology and Economics," Department of Economics, Working Paper Series, Department of Economics, Institute for Business and Economic Research, UC Berkeley qt8jd5z5j2, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    10. Rainer Hegselmann & Ulrich Krause, 2006. "Truth and Cognitive Division of Labour: First Steps Towards a Computer Aided Social Epistemology," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(3), pages 10.
    11. Guillaume Deffuant, 2006. "Comparing Extremism Propagation Patterns in Continuous Opinion Models," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 9(3), pages 8.
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