How do people make decisions between an immediate but small reward and a delayed but large one? The outcome of such decisions indicates that people discount rewards by their delay and hence these outcomes are well described by discounting functions. However, to understand irregular decisions and dysfunctional behavior one needs models which describe how the process of making the decision unfolds dynamically over time: how do we reach a decision and how do sequential decisions influence one another? Here, we present an attractor model that integrates into and extends discounting functions through a description of the dynamics leading to a final choice outcome within a trial and across trials. To validate this model, we derive qualitative predictions for the intra-trial dynamics of single decisions and for the inter-trial dynamics of sequences of decisions that are unique to this type of model. We test these predictions in four experiments based on a dynamic delay discounting computer game where we study the intra-trial dynamics of single decisions via mouse tracking and the inter-trial dynamics of sequences of decisions via sequentially manipulated options. We discuss how integrating decision process dynamics within and across trials can increase our understanding of the processes underlying delay discounting decisions and, hence, complement our knowledge about decision outcomes.