Importantly, however, individual discounting decision-making profiles can be characterized using a number of different methods: modeling the temporal discounting function via nonlinear regression, area-under-the-curve analysis, or simply the proportion of impulsive choices (Green & Myerson, 2004; Mazur, 1987; Mitchell, Fields, D'Esposito, & Boettiger, 2005; Myerson, Green, & Warusawitharana, 2001). In terms of mathematical models, the most widely used approach is a hyperbolic single parameter model (Mazur, 1987), but hyperbola-like (hyperboloid) two-parameter models can also be applied (Laibson, 1997; Myerson & Green, 1995) and an additive-utility model has recently been proposed (Killeen, 2009). These models seek to quantitatively capture the typical form of the discounting curve, namely, that the value of a delayed reward rapidly loses its value during initial delays and then decays at a more moderate rate across subsequent delays. For example, in the hyperbolic discounting curves in Figure 1, in comparing the slope during the first month of delay and the slope from 11 to 12 months of delay, it is clear that although the absolute delay durations are identical, the devaluation applied in the short run is
