How fragile are information cascades?.

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

It is well known that sequential decision making may lead to informationcascades. That is, when agents make decisions based on their privateinformation, as well as observing the actions of those before them, then itmight be rational to ignore their private signal and imitate the action ofprevious individuals. If the individuals are choosing between a right and awrong state, and the initial actions are wrong, then the whole cascade will bewrong. This issue is due to the fact that cascades can be based on very littleinformation.

We show that if agents occasionally disregard the actions of others and basetheir action only on their private information, then wrong cascades can beavoided. Moreover, we study the optimal asymptotic rate at which the errorprobability at time $t$ can go to zero. The optimal policy is for the player attime $t$ to follow their private information with probability $p_{t} = c/t$,leading to a learning rate of $c'/t$, where the constants $c$ and $c'$ areexplicit.

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