Exponential discounting | Hyperbolic discounting | |
---|---|---|

No time scaling | ||

Time scaling |

SV is the subjective value,

*A*is the amount of options,*k*is the discounting factor that multiplies the value of reward,*D*is the time delay, and*k*is the degree of discounting. The scaling parameter*s*in the lower exponential discounting equation describes scaling of individual differences in delay and*k*(Loewenstein and Prelec, 1992; Rachlin, 1989; Green and Myerson, 2004; McKerchar et al., 2009; Peters et al., 2012). For hyperbolic discounting, scaling either affects just the time delay or it additionally considers*k*. Note that when*s*= 1, there is no time scaling, or in other words, the model with time scaling equals the model without scaling. When*s*is <1, the SV is more sensitive to changes at shorter delays and less sensitive to changes at longer delays (Frederick et al., 2002).