How fragile are information cascades?

Yuval Peres, Miklós Z. Rácz, Allan Sly, Izabella Stuhl

Research output: Contribution to journalArticlepeer-review

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 pt = c/t, leading to a learning rate of c′/t, where the constants c and c′ are explicit.

Original languageEnglish (US)
Pages (from-to)2796-2814
Number of pages19
JournalAnnals of Applied Probability
Volume30
Issue number6
DOIs
StatePublished - Dec 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Asymptotic learning
  • Fragility
  • Information cascades
  • Optimal learning rate
  • Sequential decision making

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