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December 2020 How fragile are information cascades?
Yuval Peres, Miklós Z. Rácz, Allan Sly, Izabella Stuhl
Ann. Appl. Probab. 30(6): 2796-2814 (December 2020). DOI: 10.1214/20-AAP1573

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.

Citation

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Yuval Peres. Miklós Z. Rácz. Allan Sly. Izabella Stuhl. "How fragile are information cascades?." Ann. Appl. Probab. 30 (6) 2796 - 2814, December 2020. https://doi.org/10.1214/20-AAP1573

Information

Received: 1 April 2018; Revised: 1 July 2019; Published: December 2020
First available in Project Euclid: 14 December 2020

Digital Object Identifier: 10.1214/20-AAP1573

Subjects:
Primary: 60C05, 91A26

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 6 • December 2020
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