Table 1.

Theory	Normative Principle	Decision Formula	Discounting Form	Steepness parameter
DUT	Stationary time preference	Choose max(r(t)D(t)); D(t) = exp(−kt)	Exponential	Free-fit
OFT	Future reward-rate maximization	$Choose\text{ max}(\frac{r_i}{ITI+t_i})$	Hyperbolic	Inter-trial interval
ERT	Local reward- rate maximization	$Choose\text{ max}(\frac{r_i}{t_i})$	Hyperbolic	Delay to reward
TIMERR	Experientially- bounded reward-rate maximization	$Choose\text{ max}(\frac{r+R}{t+T_{\mathit{\text{ime}}}})$	Hyperbolic	Past integration interval