IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1904.08131.html

Averaging plus Learning Models and Their Asymptotics

Author

Listed:
  • Ionel Popescu
  • Tushar Vaidya

Abstract

We develop original models to study interacting agents in financial markets and in social networks. Within these models randomness is vital as a form of shock or news that decays with time. Agents learn from their observations and learning ability to interpret news or private information in time-varying networks. Under general assumption on the noise, a limit theorem is developed for the generalised DeGroot framework for certain type of conditions governing the learning. In this context, the agents beliefs (properly scaled) converge in distribution that is not necessarily normal. Fresh insights are gained not only from proposing a new setting for social learning models but also from using different techniques to study discrete time random linear dynamical systems.

Suggested Citation

  • Ionel Popescu & Tushar Vaidya, 2019. "Averaging plus Learning Models and Their Asymptotics," Papers 1904.08131, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:1904.08131
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1904.08131
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Song, Yangbo, 2016. "Social learning with endogenous observation," Journal of Economic Theory, Elsevier, vol. 166(C), pages 324-333.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    4. Sobel, Joel, 2000. "Economists' Models of Learning," Journal of Economic Theory, Elsevier, vol. 94(2), pages 241-261, October.
    5. Rabi Bhattacharya & Mukul Majumdar, 2003. "Random dynamical systems: a review," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 13-38, December.
    6. Lones Smith & Peter Sorensen, 2000. "Pathological Outcomes of Observational Learning," Econometrica, Econometric Society, vol. 68(2), pages 371-398, March.
    7. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(3), pages 909-968.
    8. Arun G. Chandrasekhar & Horacio Larreguy & Juan Pablo Xandri, 2015. "Testing Models of Social Learning on Networks: Evidence from a Lab Experiment in the Field," NBER Working Papers 21468, National Bureau of Economic Research, Inc.
    9. Daron Acemoglu & Asuman Ozdaglar, 2011. "Opinion Dynamics and Learning in Social Networks," Dynamic Games and Applications, Springer, vol. 1(1), pages 3-49, March.
    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. ,, 2013. "A general framework for rational learning in social networks," Theoretical Economics, Econometric Society, vol. 8(1), January.
    12. 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.
    13. Bikhchandani, Sushil & Hirshleifer, David & Welch, Ivo, 1992. "A Theory of Fads, Fashion, Custom, and Cultural Change in Informational Cascades," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 992-1026, October.
    14. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    15. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
    16. Abhijit Banerjee & Emily Breza & Arun G. Chandrasekhar & Markus Mobius, 2021. "Naïve Learning with Uninformed Agents," American Economic Review, American Economic Association, vol. 111(11), pages 3540-3574, November.
    17. Alan Kirman, 2002. "Reflections on interaction and markets," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 322-326.
    18. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 797-817.
    Full references (including those not matched with items on IDEAS)

    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. Michel Grabisch & Agnieszka Rusinowska, 2020. "A Survey on Nonstrategic Models of Opinion Dynamics," Games, MDPI, vol. 11(4), pages 1-29, December.
    3. Daron Acemoglu & Asuman Ozdaglar, 2011. "Opinion Dynamics and Learning in Social Networks," Dynamic Games and Applications, Springer, vol. 1(1), pages 3-49, March.
    4. Pietro Battiston & Luca Stanca, 2014. "Boundedly Rational Opinion Dynamics in Directed Social Networks: Theory and Experimental Evidence," Working Papers 267, University of Milano-Bicocca, Department of Economics, revised Jan 2014.
    5. Dasaratha, Krishna & He, Kevin, 2020. "Network structure and naive sequential learning," Theoretical Economics, Econometric Society, vol. 15(2), May.
    6. Ding, Huihui & Pivato, Marcus, 2021. "Deliberation and epistemic democracy," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 138-167.
    7. Jan Hązła & Ali Jadbabaie & Elchanan Mossel & M. Amin Rahimian, 2021. "Bayesian Decision Making in Groups is Hard," Operations Research, INFORMS, vol. 69(2), pages 632-654, March.
    8. , & ,, 2015. "Information diffusion in networks through social learning," Theoretical Economics, Econometric Society, vol. 10(3), September.
    9. Catherine A. Glass & David H. Glass, 2021. "Social Influence of Competing Groups and Leaders in Opinion Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 799-823, October.
    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. Drehmann, Mathias & Oechssler, Jorg & Roider, Andreas, 2007. "Herding with and without payoff externalities -- an internet experiment," International Journal of Industrial Organization, Elsevier, vol. 25(2), pages 391-415, April.
    12. Michel Grabisch & Antoine Mandel & Agnieszka Rusinowska & Emily Tanimura, 2015. "Strategic influence in social networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01158168, HAL.
    13. 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.
    14. Pooya Molavi & Ceyhun Eksin & Alejandro Ribeiro & Ali Jadbabaie, 2016. "Learning to Coordinate in Social Networks," Operations Research, INFORMS, vol. 64(3), pages 605-621, June.
    15. Davide Crapis & Bar Ifrach & Costis Maglaras & Marco Scarsini, 2017. "Monopoly Pricing in the Presence of Social Learning," Management Science, INFORMS, vol. 63(11), pages 3586-3608, November.
    16. Abhijit Banerjee & Olivier Compte, 2024. "Consensus and Disagreement: Information Aggregation under (Not So) Naive Learning," Journal of Political Economy, University of Chicago Press, vol. 132(8), pages 2790-2829.
    17. Delia Coculescu & Médéric Motte & Huyên Pham, 2024. "Opinion dynamics in communities with major influencers and implicit social influence via mean-field approximation," Mathematics and Financial Economics, Springer, volume 18, number 7, June.
    18. Mueller-Frank, Manuel, 2014. "Does one Bayesian make a difference?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 423-452.
    19. Christoph March, 2011. "Adaptive social learning," Working Papers halshs-00572528, HAL.
    20. Fernandes, Marcos R., 2023. "Confirmation bias in social networks," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 59-76.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:1904.08131. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.