Social Learning in a Changing World

  • Rafael M. Frongillo
  • Grant Schoenebeck
  • Omer Tamuz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)


We study a model of learning on social networks in dynamic environments, describing a group of agents who are each trying to estimate an underlying state that varies over time, given access to weak signals and the estimates of their social network neighbors.

We study three models of agent behavior. In the fixed response model, agents use a fixed linear combination to incorporate information from their peers into their own estimate. This can be thought of as an extension of the DeGroot model to a dynamic setting. In the best response model, players calculate minimum variance linear estimators of the underlying state.

We show that regardless of the initial configuration, fixed response dynamics converge to a steady state, and that the same holds for best response on the complete graph. We show that best response dynamics can, in the long term, lead to estimators with higher variance than is achievable using well chosen fixed responses.

The penultimate prediction model is an elaboration of the best response model. While this model only slightly complicates the computations required of the agents, we show that in some cases it greatly increases the efficiency of learning, and on complete graphs is in fact optimal, in a strong sense.


social networks Bayesian agents social learning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aaronson, S.: The complexity of agreement. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, STOC 2005, pp. 634–643. ACM (2005)Google Scholar
  2. 2.
    Acemoglu, D., Dahleh, M., Lobel, I., Ozdaglar, A.: Bayesian learning in social networks (2008)Google Scholar
  3. 3.
    Acemoglu, D., Nedic, A., Ozdaglar, A.: Convergence of rule-of-thumb learning rules in social networks. In: 47th IEEE Conference on Decision and Control, CDC 2008, pp. 1714–1720. IEEE (2008)Google Scholar
  4. 4.
    Aumann, R.J.: Agreeing to disagree. The Annals of Statistics 4(6), 1236–1239 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bachelier, L.: Théorie de la spéculation. Gauthier-Villars (1900)Google Scholar
  6. 6.
    Bala, V., Goyal, S.: Learning from neighbours. Review of Economic Studies 65(3), 595–621 (1998), CrossRefzbMATHGoogle Scholar
  7. 7.
    Bandiera, O., Rasul, I.: Social networks and technology adoption in northern mozambique*. The Economic Journal 116(514), 869–902 (2006)CrossRefGoogle Scholar
  8. 8.
    Besley, T., Case, A.: Diffusion as a learning process: Evidence from hyv cotton (1994) Working PapersGoogle Scholar
  9. 9.
    Conley, T., Udry, C.: Social learning through networks: The adoption of new agricultural technologies in ghana. American Journal of Agricultural Economics 83(3), 668–673 (2001)CrossRefGoogle Scholar
  10. 10.
    DeGroot, M.H.: Reaching a consensus. Journal of the American Statistical Association, 118–121 (1974)Google Scholar
  11. 11.
    DeMarzo, P., Vayanos, D., Zwiebel, J.: Persuasion bias, social influence, and unidimensional opinions. Quarterly Journal of Economics 118, 909–968 (2003)CrossRefzbMATHGoogle Scholar
  12. 12.
    Frongillo, R.M., Schoenebeck, G., Tamuz, O.: Social learning in a changing world. Tech. rep. (September 2011),
  13. 13.
    Gale, D., Kariv, S.: Bayesian learning in social networks. Games and Economic Behavior 45(2), 329–346 (2003), MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Geanakoplos, J.: Common knowledge. In: Proceedings of the 4th Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 254–315. Morgan Kaufmann Publishers Inc. (1992)Google Scholar
  15. 15.
    Geanakoplos, J.D., Polemarchakis, H.M.: We can’t disagree forever* 1. Journal of Economic Theory 28(1), 192–200 (1982)CrossRefzbMATHGoogle Scholar
  16. 16.
    Jackson, M.O.: The economics of social networks. In: Blundell, R., Newey, W., Persson, T. (eds.) Theory and Applications: Ninth World Congress of the Econometric Society. Advances in Economics and Econometrics, vol. I, pp. 1–56. Cambridge University Press (2006)Google Scholar
  17. 17.
    Jadbabaie, A., Sandroni, A., Tahbaz-Salehi, A.: Non-bayesian social learning, second version. Pier working paper archive, Penn Institute for Economic Research, Department of Economics. University of Pennsylvania (2010)Google Scholar
  18. 18.
    Kalman, R., et al.: A new approach to linear filtering and prediction problems. Journal of basic Engineering 82(1), 35–45 (1960)CrossRefGoogle Scholar
  19. 19.
    Kohler, H.P.: Learning in social networks and contraceptive choice. Demography 34(3), 369–383 (1997)MathSciNetCrossRefGoogle Scholar
  20. 20.
    McKelvey, R.D., Page, T.: Common knowledge, consensus, and aggregate information. Econometrica: Journal of the Econometric Society, 109–127 (1986)Google Scholar
  21. 21.
    Mossel, E., Tamuz, O.: Efficient bayesian learning in social networks with gaussian estimators. Tech. rep. (September 2010),
  22. 22.
    Mossel, E., Tamuz, O.: Iterative maximum likelihood on networks. Advances in Applied Mathematics 45(1), 36–49 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Parikh, R., Krasucki, P.: Communication, consensus, and knowledge* 1. Journal of Economic Theory 52(1), 178–189 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Simon, H.: Reason in Human Affairs. Stanford University Press (1982)Google Scholar
  25. 25.
    Smith, L., Sørensen, P.: Pathological outcomes of observational learning. Econometrica 68(2), 371–398 (2000)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rafael M. Frongillo
    • 1
  • Grant Schoenebeck
    • 2
  • Omer Tamuz
    • 3
  1. 1.Computer Science DepartmentUniversity of CaliforniaBerkeleyUSA
  2. 2.Computer Science DepartmentPrinceton UniversityUSA
  3. 3.Weizmann InstituteIsrael

Personalised recommendations