Discounting in Pigeons When the Choice is between Two Delayed Rewards: Implications for Species Comparisons

Abstract

Studies of delay discounting typically have involved choices between smaller, immediate outcomes and larger, delayed outcomes. In a study of delay discounting in humans, Green et al. (2005) added a period of time prior to both outcomes, creating a delay common to both. They found that the subjective value of the more delayed reward was well described by a hyperboloid discounting function and that the degree to which that outcome was discounted decreased as the common delay increased. In two experiments, we examined the effect of adding a common delay on the discounting of food rewards in pigeons. In Experiment 1, an adjusting-amount procedure was used to establish discounting functions when the common delay was 0, 3, 5, and 10 s, and different stimuli signaled time to the smaller, sooner and larger, later rewards. In contrast to humans, the pigeons showed increases in the degree of discounting when a common delay was added. In Experiment 2, the delay common to both rewards and the delay unique to the larger, later reward were each specifically signaled. With this procedure, the degree of discounting decreased as the common delay increased, a result consistent with that obtained with humans (Green et al., 2005). These findings reveal fundamental similarities between pigeons' and humans' choice behavior, and provide strong interspecies support for the hypothesis that choice between delayed outcomes is based on comparison of their hyperbolically discounted present subjective values.

Keywords: delay discounting; discounting function; humans; hyperbolic; pigeons.

Figure 1

Hyperboloid discounting of smaller, sooner and larger, later rewards. The x-axis represents the time until a reward, and the y-axis represents its subjective value. The portion of the delay that is common to both the smaller, sooner and larger, later rewards is labeled A, and the portion of the delay to the larger, later reward that is unique is labeled B.

Figure 2

Discounting of the larger, later reward in the 0-, 3-, 5-, and 10-s common-delay conditions in Experiment 1. Symbols represent subjective values (in pellets) for the four common-delay conditions. Curves represent the best-fitting discounting functions (Eq. 1).

Figure 3

Procedures for Experiments 1 and 2. SD and LD refer to the shorter and longer delays to reinforcement; CD refers to the portion of the delay to the smaller, sooner and larger, later rewards that they have in common, and UD refers to the portion of the delay to the larger, later reward that is unique to that reward. The circles at the top represent the response keys (R = red; G = green), the rectangles represent the cue lights, and the light bulbs represent the flashing house light.

Figure 4

Discounting of the larger, later reward in the 5-, 10-, and 20-s common-delay conditions in Experiment 2. The data for the 0-s common-delay condition are replotted from Experiment 1. Symbols represent subjective values (in pellets) for the four common-delay conditions. Curves represent the best-fitting discounting functions (Eq.1).

Figure 5

Area under the discounting curve for each common-delay condition for each pigeon in Experiments 1 and 2. Shallower discounting is indicated by higher values.

Figure 6

Subjective value of the larger, later reward in the final series of replications for each pigeon in Experiment 2. CD/UD refers to the signaling procedure introduced in Experiment 2, and SD/LD refers to replications using the signaling procedure originally used in Experiment 1. Note that the common and unique delays were different for each pigeon.