Dual process theories of decision making describe choice as the product of an automatic System 1,
which is quick to activate but behaves impulsively, and a deliberative System 2, which is slower to
activate but makes decisions in a rational and controlled manner. However, most existent dual
process theories are not mathematically specified, and thus do not generate testable qualitative and
quantitative predictions. For intertemporal choices, notable exceptions have been proposed by
Fudenberg & Levine (2006) and Loewenstein et al. (2015). None of them provide a formal
specification regarding the dynamics of the interplay of the two systems. The here proposed dynamic
dual process model takes this into account; it makes precise predictions regarding choice probability
and response time distributions. Using simulation studies, I illustrate how different factors (timing of
System 1, time constraint, preferences construction functions in both systems, and architecture)
influence model predictions. The modelling framework provides a mathematical approach that may
bring novel insights regarding the processes underlying intertemporal choices.