Collaborative interactions require social robots to adapt to the dynamics of human affective behaviour. Yet, current approaches for affective behaviour generation in robots focus on instantaneous perception to generate a one-to-one mapping between observed human expressions and static robot actions. In this paper, we propose a novel framework for personality-driven behaviour generation in social robots. The framework consists of (i) a hybrid neural model for evaluating facial expressions and speech, forming intrinsic affective representations in the robot, (ii) an Affective Core, that employs self-organising neural models to embed robot personality traits like patience and emotional actuation, and (iii) a Reinforcement Learning model that uses the robot's affective appraisal to learn interaction behaviour. For evaluation, we conduct a user study (n = 31) where the NICO robot acts as a proposer in the Ultimatum Game. The effect of robot personality on its negotiation strategy is witnessed by participants, who rank a patient robot with high emotional actuation higher on persistence, while an inert and impatient robot higher on its generosity and altruistic behaviour.