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How fragile are information cascades?

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  • Yuval Peres
  • Miklos Z. Racz
  • Allan Sly
  • Izabella Stuhl

Abstract

It is well known that sequential decision making may lead to information cascades. That is, when agents make decisions based on their private information, as well as observing the actions of those before them, then it might be rational to ignore their private signal and imitate the action of previous individuals. If the individuals are choosing between a right and a wrong state, and the initial actions are wrong, then the whole cascade will be wrong. This issue is due to the fact that cascades can be based on very little information. We show that if agents occasionally disregard the actions of others and base their action only on their private information, then wrong cascades can be avoided. Moreover, we study the optimal asymptotic rate at which the error probability at time $t$ can go to zero. The optimal policy is for the player at time $t$ to follow their private information with probability $p_{t} = c/t$, leading to a learning rate of $c'/t$, where the constants $c$ and $c'$ are explicit.

Suggested Citation

  • Yuval Peres & Miklos Z. Racz & Allan Sly & Izabella Stuhl, 2017. "How fragile are information cascades?," Papers 1711.04024, arXiv.org, revised Feb 2018.
  • Handle: RePEc:arx:papers:1711.04024
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    References listed on IDEAS

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    4. 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.
    5. Bogaçhan Çelen & Shachar Kariv, 2004. "Distinguishing Informational Cascades from Herd Behavior in the Laboratory," American Economic Review, American Economic Association, vol. 94(3), pages 484-498, June.
    6. Anderson, Lisa R & Holt, Charles A, 1997. "Information Cascades in the Laboratory," American Economic Review, American Economic Association, vol. 87(5), pages 847-862, December.
    7. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 107(3), pages 797-817.
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