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Bayesian Learning in Social Networks

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  • Daron Acemoglu
  • Munther A. Dahleh
  • Ilan Lobel
  • Asuman Ozdaglar

Abstract

We study the perfect Bayesian equilibrium of a model of learning over a general social network. Each individual receives a signal about the underlying state of the world, observes the past actions of a stochastically-generated neighborhood of individuals, and chooses one of two possible actions. The stochastic process generating the neighborhoods defines the network topology (social network). The special case where each individual observes all past actions has been widely studied in the literature. We characterize pure-strategy equilibria for arbitrary stochastic and deterministic social networks and characterize the conditions under which there will be asymptotic learning -- that is, the conditions under which, as the social network becomes large, individuals converge (in probability) to taking the right action. We show that when private beliefs are unbounded (meaning that the implied likelihood ratios are unbounded), there will be asymptotic learning as long as there is some minimal amount of "expansion in observations". Our main theorem shows that when the probability that each individual observes some other individual from the recent past converges to one as the social network becomes large, unbounded private beliefs are sufficient to ensure asymptotic learning. This theorem therefore establishes that, with unbounded private beliefs, there will be asymptotic learning an almost all reasonable social networks. We also show that for most network topologies, when private beliefs are bounded, there will not be asymptotic learning. In addition, in contrast to the special case where all past actions are observed, asymptotic learning is possible even with bounded beliefs in certain stochastic network topologies.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14040.

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Date of creation: May 2008
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Handle: RePEc:nbr:nberwo:14040

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Cited by:
  1. 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.
  2. Anthony Ziegelmeyer & Frédéric Koessler & Juergen Bracht & Eyal Winter, 2010. "Fragility of information cascades: an experimental study using elicited beliefs," Experimental Economics, Springer, vol. 13(2), pages 121-145, June.
  3. 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.
  4. Marco Pelliccia, 2013. "Ambiguous Networks," Birkbeck Working Papers in Economics and Finance 1303, Birkbeck, Department of Economics, Mathematics & Statistics.
  5. Corazzini, Luca & Pavesi, Filippo & Petrovich, Beatrice & Stanca, Luca, 2012. "Influential listeners: An experiment on persuasion bias in social networks," European Economic Review, Elsevier, vol. 56(6), pages 1276-1288.
  6. FORSTER, Manuel & MAULEON, Ana & VANNETELBOSCH, Vincent, 2013. "Trust and manipulation in social networks," CORE Discussion Papers 2013050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Acemoglu, Daron & Ozdaglar, Asuman & ParandehGheibi, Ali, 2010. "Spread of (mis)information in social networks," Games and Economic Behavior, Elsevier, vol. 70(2), pages 194-227, November.
  8. Opolot, Daniel, 2012. "Social interactions and complex networks," MERIT Working Papers 014, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
  9. Junjie Zhou & Ying-Ju Chen, 2013. "Targeted information release in social networks," Working Papers 13-04, NET Institute.
  10. Gabriel Galand, 2009. "The Neutrality of Money Revisited with a Bottom-Up Approach: Decentralisation, Limited Information and Bounded Rationality," Computational Economics, Society for Computational Economics, vol. 33(4), pages 337-360, May.
  11. Büchel, Berno & Hellmann, Tim & Klößner, Stefan, 2013. "Opinion Dynamics under Conformity," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79770, Verein für Socialpolitik / German Economic Association.
  12. repec:dgr:unumer:2012014 is not listed on IDEAS
  13. Ilan Lobel & Evan Sadler, 2013. "Preferences, Homophily, and Social Learning," Working Papers 13-01, NET Institute.
  14. Opolot, Daniel & Azomahou, Theophile, 2012. "Learning and convergence in networks," MERIT Working Papers 074, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).

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