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_15: We analyze a sequential decision model in which each decision maker looks at the decisions made by previous decision makers in taking her own decision. This is rational for her because these other decision makers may have some information that is important for her. We then show that the decision rules that are chosen by optimizing individuals will be characterized by herd behavior; i.e., people will be doing what others are doing rather than using their information. We then show that the resulting equilibrium is inefficient.
@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.
The special case of the model described in the previous subsection where every agent is Bayesian (i.e., with @math for every @math ) is identical to the model described in the exposition of Easley and Kleinberg [Chapter 16] easley2010networks . The original model of Bikhchandani, Hirshleifer, and Welch @cite_11 differs only in its tie-breaking rule (breaking ties by flipping a fair coin), while that of Banerjee @cite_15 differs in the signal distribution (false signals are drawn from a continuous distribution). Despite these minor differences, these models all share the same phenomenological behavior as described in the introductory paragraphs.