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Bayesian Social Learning with Local Interactions

Author

Listed:
  • Antonio Guarino

    (Department of Economics ELSE, University College London, London WC1E 6BT, UK)

  • Antonella Ianni

    () (Economic Division, School of Social Sciences, University of Southampton, Southampton SO17 1BJ, UK)

Abstract

We study social learning in a large population of agents who only observe the actions taken by their neighbours. Agents have to choose one, out of two, reversible actions, each optimal in one, out of two, unknown states of the world. Each agent chooses rationally, on the basis of private information and of the observation of his neighbours’ actions. Agents can repeatedly update their choices at revision opportunities that they receive in a random sequential order. We show that if agents receive equally informative signals and observe both neighbours, then actions converge exponentially fast to a configuration where some agents are permanently wrong. In contrast, if agents are unequally informed (in that some agents receive a perfectly informative signal and others are uninformed) and observe one neighbour only, then everyone will eventually choose the correct action. Convergence, however, obtains very slowly, at rate √t.

Suggested Citation

  • Antonio Guarino & Antonella Ianni, 2010. "Bayesian Social Learning with Local Interactions," Games, MDPI, Open Access Journal, vol. 1(4), pages 1-21, October.
  • Handle: RePEc:gam:jgames:v:1:y:2010:i:4:p:438-458:d:9932
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    References listed on IDEAS

    as
    1. Antonio Guarino & Philippe Jehiel, 2009. "Social Leanring with Course Inference," WEF Working Papers 0050, ESRC World Economy and Finance Research Programme, Birkbeck, University of London.
    2. Gale, Douglas & Kariv, Shachar, 2003. "Bayesian learning in social networks," Games and Economic Behavior, Elsevier, vol. 45(2), pages 329-346, November.
    3. Antonio Guarino & Philippe Jehiel, 2013. "Social Learning with Coarse Inference," American Economic Journal: Microeconomics, American Economic Association, vol. 5(1), pages 147-174, February.
    4. 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.
    5. Peter M. DeMarzo & Dimitri Vayanos & Jeffrey Zwiebel, 2003. "Persuasion Bias, Social Influence, and Unidimensional Opinions," The Quarterly Journal of Economics, Oxford University Press, vol. 118(3), pages 909-968.
    6. Antonio Guarino & Steffen Huck & Heike Harmgart, 2008. "When half the truth is better than the truth: A Theory of aggregate information cascades," WEF Working Papers 0046, ESRC World Economy and Finance Research Programme, Birkbeck, University of London.
    7. Darrell Duffie & Gustavo Manso, 2007. "Information Percolation in Large Markets," American Economic Review, American Economic Association, vol. 97(2), pages 203-209, May.
    8. Devenow, Andrea & Welch, Ivo, 1996. "Rational herding in financial economics," European Economic Review, Elsevier, vol. 40(3-5), pages 603-615, April.
    9. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 107(3), pages 797-817.
    10. Callander, Steven & Hörner, Johannes, 2009. "The wisdom of the minority," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1421-1439.2, July.
    11. Chamley,Christophe P., 2004. "Rational Herds," Cambridge Books, Cambridge University Press, number 9780521530927, March.
    12. Celen, Bogachan & Kariv, Shachar, 2004. "Observational learning under imperfect information," Games and Economic Behavior, Elsevier, vol. 47(1), pages 72-86, April.
    13. Gale, Douglas, 1996. "What have we learned from social learning?," European Economic Review, Elsevier, vol. 40(3-5), pages 617-628, April.
    14. Chamley,Christophe P., 2004. "Rational Herds," Cambridge Books, Cambridge University Press, number 9780521824019, March.
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    Citations

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    Cited by:

    1. Ilan Lobel & Evan Sadler, 2013. "Preferences, Homophily, and Social Learning," Working Papers 13-01, NET Institute.
    2. Lobel, Ilan & Sadler, Evan, 2015. "Information diffusion in networks through social learning," Theoretical Economics, Econometric Society, vol. 10(3), September.

    More about this item

    Keywords

    social learning; Bayesian learning; local informational externalities; path dependence; consensus; clustering; convergence rates;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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