Observational Learning in Random Networks

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4539)


In the standard model of observational learning, n agents sequentially decide between two alternatives a or b, one of which is objectively superior. Their choice is based on a stochastic private signal and the decisions of others. Assuming a rational behavior, it is known that informational cascades arise, which cause an overwhelming fraction of the population to make the same choice, either correct or false. Assuming that each agent is able to observe the actions of all predecessors, it was shown by Bikhchandani, Hirshleifer, and Welch [1,2] that, independently of the population size, false informational cascades are quite likely.

In a more realistic setting, agents observe just a subset of their predecessors, modeled by a random network of acquaintanceships. We show that the probability of false informational cascades depends on the edge probability p of the underlying network. As in the standard model, the emergence of false cascades is quite likely if p does not depend on n. In contrast to that, false cascades are very unlikely if p = p(n) is a sequence that decreases with n. Provided the decay of p is not too fast, correct cascades emerge almost surely, benefiting the entire population.


Social Network Decision Rule Random Graph Random Network Correct Choice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bikhchandani, S., Hirshleifer, D., Welch, I.: A theory of fads, fashion, custom, and cultural change in informational cascades. Journal of Political Economy 100(5), 992–1026 (1992)CrossRefGoogle Scholar
  2. Bikhchandani, S., Hirshleifer, D., Welch, I.: Learning from the behavior of others: Conformity, fads, and informational cascades. The. Journal of Economic Perspectives 12(3), 151–170 (1998)Google Scholar
  3. Banerjee, A.V.: A simple model of herd behavior. The. Quarterly Journal of Economics 107(3), 797–817 (1992)CrossRefGoogle Scholar
  4. Surowiecki, J.: The Wisdom of Crowds. Anchor (2005)Google Scholar
  5. Brin, S., Page, L.: The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems 30(1–7), 107–117 (1998)CrossRefGoogle Scholar
  6. Erdős, P., Rényi, A.: On random graphs. Publ. Math. Debrecen 6, 290–297 (1959)MathSciNetGoogle Scholar
  7. Bollobás, B.: Random graphs, 2nd edn. Cambridge Studies in Advanced Mathematics, vol. 73. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar
  8. Janson, S., Łuczak, T., Rucinski, A.: Random graphs. In: Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience, New York (2000)Google Scholar
  9. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)CrossRefMathSciNetGoogle Scholar
  10. Çelen, B., Kariv, S.: Observational learning under imperfect information. Games Econom. Behav. 47(1), 72–86 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  11. Banerjee, A., Fudenberg, D.: Word-of-mouth learning. Games Econom. Behav. 46(1), 1–22 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. Gale, D., Kariv, S.: Bayesian learning in social networks. Games Econom. Behav. 45(2), 329–346, Special issue in honor of Rosenthal, R. W. (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  13. Watts, D.J.: A simple model of global cascades on random networks. In: Proc. Natl. Acad. Sci. USA 99(9), 5766–5771(electronic) (2002)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Institute of Theoretical Computer Science, ETH Zurich, 8092 ZurichSwitzerland

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