A Binary Signal Model for Herding Behaviour with Imprecise Probabilities

The paper addresses uncertainty analysis in decision theory, by applying Imprecise Probabilities to a Herding Behaviour model, which describes imitative behaviour and explains the informational cascades phenomenon in the financial market. In the literature, the application of the principle of rationality in herding behaviour generates informational cascades, i. e. sequences of actions in which each agent makes his choice by observing the decisions taken by those who acted before him, regardless of the private signal he owns. Since the probability distribution of the signal may be hard to identify in some cases, our paper studies the herding behaviour 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. We aim to test the herding behaviour 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.