On the robustness of informational cascades with imprecise binary signals

The paper addresses uncertainty analysis in decision theory by applying imprecise probabilities to a herding behavior model, which describes imitative behavior and explains the informational cascade phenomenon. In the literature, the application of the principle of rationality in herding behavior generates informational cascades, i. e., sequences of actions in which each agent makes their choice by observing the decisions taken by those who acted before them, regardless of the private signal they own. Since the probability distribution of the signal may be hard to identify in some cases, this paper studies the herding behavior model by considering imprecise the signal probability. In the simplest case of a binary signal model, the agent's private information is described by using a set of probability measures and assuming that the signal probability ranges in a probability interval. The paper aims to test the herding behavior model robustness when some assumptions no longer hold due to imprecise probabilities and prove that an informational cascade may occur even with a further noisy signal.