Autonomous vehicles (AVs), also called self-driving cars" that are appearing on the roads need a better understanding of pedestrians' social behaviour, especially in urban areas. Previous work showed that pedestrians may take advantage over autonomous vehicles by intentionally and constantly stepping in front of AVs, hence preventing them from making progress on the roads. This inability of current AVs to read the intention of other road users, predict their future behaviour and interact with them is known asthe big problem with self-driving cars". A comprehensive review of existing pedestrian models for AVs, ranging from low-level sensing, detection and tracking models to high-level interaction and game theoretic models of pedestrian behaviour, found that the lower-level models are accurate and mature enough to be deployed on AVs but more research is needed in the higher-level models. Hence, in this work, we focus on modelling, learning and operating pedestrian behaviour on self-driving cars. Game theory is a framework that has been widely used to model decision-making between rational agents, especially in economics and in multi-agent systems coordination. We here propose a game theory model, a discrete sequential model for negotiations between an AV and a pedestrian at an unsignalized intersection To validate this model, we ran several experiments with human participants to infer the utility parameters using Gaussian process regression. We also learned from current pedestrian--vehicle interactions using a large-scale dataset from real-world human road crossings at an intersection. Moreover, we recently developed the first mathematical model of proxemics and trust concept for self-driving cars and pedestrians interactions. We now plan to implement this model on OpenPodcar, a low-cost and open source autonomous vehicle research platform that we developed and that will be used for real-world tests.