Table 1.

Listed are the five SV discounting models: exponential and hyperbolic discounting, either with or without second scaling

Exponential discountingHyperbolic discounting
No time scalingSV=A*exp(kD) SV=A(1+kD)
Time scalingSV=A*exp((kD)s) SV=A1+k*Ds or SV=A(1+kD)s
  • 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).