HOW FRAGILE ARE INFORMATION CASCADES?

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 previou...

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Bibliographic Details
Published in:The Annals of applied probability 2020-12, Vol.30 (6), p.2796-2814
Main Authors: Peres, Yuval, Rácz, Miklós Z., Sly, Allan, Stuhl, Izabella
Format: Article
Language:English
Subjects:
Cascades
Decision making
Information
Learning
Probability
Probability distribution
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Summary: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.
ISSN:1050-5164
2168-8737
DOI:10.1214/20-AAP1573