Figure 5.

The semi-Markov model of hyperbolic discounting (without distributed discounting) cannot produce precommitment behavior. (A) At the selected parameters, SS was preferred to LL and C was preferred to N. This bar graph represents the same data as (B) at R_S = 3.46. (B) As R_S increased, the preference for C overtook N exactly at the same point as the preference for SS overtook LL, meaning that this model would not precommit to avoid an impulsive choice. Note that in this model, each state has a long temporal extent (and replacing long states with one-step states produces different discounting), so it is not possible to plot intermediate discounted values as in Figures 2C, 3C, and 4C.