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 @math can go to zero. The optimal policy is for the player at time @math to follow their private information with probability @math , leading to a learning rate of @math , where the constants @math and @math are explicit.
@cite_11: An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow the behavior of the preceding individual without regard to his own information. We argue that localized conformity of behavior and the fragility of mass behaviors can be explained by informational cascades.
In particular, Bikhchandani et al. @cite_11 emphasize the of information cascades with respect to different types of shocks, as prior work on conforming behavior could not explain this phenomenon. They show examples from numerous fields (e.g., politics, zoology, medicine, and finance) where cascades occur and are fragile. The current paper can be viewed as a more detailed quantitative exploration of the fragility of cascades. What amount of additional information is needed to break wrong cascades? What is the optimal rate of learning that can be achieved?