Mazur, J. E., & Biondi, D. R. (2009).
Delay-amount tradeoffs in choices by pigeons and rats: hyperbolic versus
exponential discounting.
Journal of the Experimental Analysis of Behavior, 91, 197-211.
An adjusting-delay procedure was used to study the choices of pigeons and rats when both delay and
amount of reinforcement were varied. In different conditions, the choice alternatives included one
versus two reinforcers, one versus three reinforcers, and three versus two reinforcers. The delay to one
alternative (the standard alternative) was kept constant in a condition, and the delay to the other (the
adjusting alternative) was increased or decreased many times a session so as to estimate an indifference
point—a delay at which the two alternatives were chosen about equally often. Indifference functions
were constructed by plotting the adjusting delay as a function of the standard delay for each pair of
reinforcer amounts. The experiments were designed to test the prediction of a hyperbolic decay
equation that the slopes of the indifference functions should increase as the ratio of the two reinforcer
amounts increased. Consistent with the hyperbolic equation, the slopes of the indifference functions
depended on the ratios of the two reinforcer amounts for both pigeons and rats. These results were not
compatible with an exponential decay equation, which predicts slopes of 1 regardless of the reinforcer
amounts. Combined with other data, these findings provide further evidence that delay discounting is
well described by a hyperbolic equation for both species, but not by an exponential equation.
Quantitative differences in the y-intercepts of the indifference functions from the two species suggested
that the rate at which reinforcer strength decreases with increasing delay may be four or five times
slower for rats than for pigeons.
Key words: reinforcer delay, reinforcer amount, hyperbolic discounting, exponential discounting, selfcontrol,
pigeons, keypeck, rats, lever press