Imprecise Probabilities in Decision Theory: applications in Herding Behaviour models

The thesis focuses on studying Game Theory and Decision Theory models under uncertainty, which is represented by imprecise probabilities. Imprecise probabilities are mathematical models describing uncertainty in the absence of classical probabilities. They are used to extend and generalise the classical Probability Theory, whenever a single probability distribution is hard to identify. This work proposes an application of imprecise probabilities to some herding behaviour models, which describe the tendency of individuals to follow other individuals and imitate their behaviour, ignoring their private information. Particular attention is addressed to the informational cascade phenomenon, based on imitative behaviour, in which after some periods an agent's action is no longer informative to other market participants. In detail, probability on the individual's private information is assumed to range in a probability interval, and it is updated with a process called Bayesian updating. The aim is to test the robustness of these models with respect to the perturbations of the probabilistic model, and investigate whether an informational cascade may occur even under uncertainty.