Steep Spatial Discounting by Free-Ranging Rhesus Macaques
“A fruit in hand is worth many more in the bush,” said Jerald Kralik, a Dartmouth psychology professor. In a recent paper entitled Steep spatial discounting by free-ranging rhesus macaques, Kralik examined the decision-making processes of animals in the wild.
Specifically, Kralik was trying to determine the tradeoff between the amount of a positive reward and the delay in receiving it. Naturally, animals tend to discount the overall value of a reward if it is not immediately available. A food source, for instance, is much more valuable if it is nearby rather than far away.
One way to model this value is by the formula V = A/(1+KD). Here, the subjective value of a reward V is equal to the absolute value (e.g. amount of food) of the reward discounted by a factor of 1 + KD, where K is a constant and D is the length of delay. Equivalently, as Kralik did in his experiment, we can let D symbolize the distance to the reward. We could model the subjective value of a reward by the similar expression V = A/(1+KDB). Here, B is some exponential parameter, and its inclusion implies that discounting does not increase linearly with delay (or distance).
Kralik sought to determine which model better represented the choices that animals make. In order to test them, Kralik conducted a survey among male rhesus macaques on the island of Cayo Santiago, Puerto Rico. The procedures of the experiment were relatively simple. The researchers placed a certain number of apple slices on two trays. The team would locate a lone individual, then place one tray near the monkey, and one tray farther away. The testing conditions, including the number of apple slices and the distances used, varied throughout the experiment. In each case, however, the number of apples on the near tray remained constant, while the number on the far tray varied.
Not surprisingly, when the amount of food on the far tray was relatively small, the monkeys preferred the closer tray almost every time. As the amount of food on the far tray increased, their decisions became more varied. Kralik’s goal, however, was not such an obvious assumption, but rather to determine the model for the monkeys’ preferences.
The first model, with the linear D term, was unable to explain the very high rate of discounting as the distance of the far tray increased.
Granted, it is difficult to draw real-world conclusions from such a “closed experiment.” Only a few meters separated the two trays of food. It is possible that the experimenters may have unsettled the monkeys. Perhaps the monkeys chose the near tray simply because it was closer, thinking they would be able to continue on to the far tray after. Nevertheless, the results suggest that the decisions of these animals follow a rational framework that can be estimated accurately with a simple model.