How fragile are information cascades?

TL;DR

This paper investigates the fragility of information cascades in sequential decision-making, showing that occasional reliance on private signals can prevent wrong cascades and analyzing the optimal learning rate for error reduction.

Contribution

It introduces a strategy where agents sometimes ignore others' actions, preventing wrong cascades, and derives explicit optimal rates for error probability decay.

Findings

Occasional disregard of others' actions prevents wrong cascades.

Optimal error decay rate is proportional to 1/t.

Explicit constants for learning rates are provided.

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.