In this article we address coverage and comprehensiveness issues raised by the integration of a large class of psychological phenomena into rational dialogical agents. These two issues are handled through the definition of a generic framework based on the notion of personality engine, which makes it possible to reify in separate modules in one hand the application-dependent parts and on the other hand the resources involved in the representation of the psychological phenomena. We introduce an enriched taxonomy of personality traits, based on the well-used ffm/neo pi-r taxonomy and we show how it can be applied on an example of agents, taken from the literature. Then we introduce the necessary concepts for modeling a personality engine. A case study, using a simplified world of dialogical agents, shows how those agents can be provided with a personality engine affecting the way they communicate with each other, and demonstrates how it can be used to implement the example. Finally, we compare our approach to other attempts at implementing personality features in rational agents.