Choice in a successive-encounters procedure and hyperbolic decay of reinforcement

Pigeons responded in a successive-encounters procedure that consisted of a search state, a choice state, and a handling state. The search state was either a fixed-interval or mixed-interval schedule presented on the center key of a three-key chamber. Upon completion of the search state, the choice state was presented, in which the center key was off and the two side keys were lit. A pigeon could either accept a delay followed by food (by pecking the right key) or reject this option and return to the search state (by pecking the left key). During the choice state, a red right key represented the long alternative (a long handling delay followed by food), and a green right key represented the short alternative (a short handling delay followed by food). In some conditions, both the short and long alternatives were fixed-time schedules, and in other conditions both were mixed-time schedules. Contrary to the predictions of both optimal foraging theory and delay-reduction theory, the percentage of trials on which pigeons accepted the long alternative depended on whether the search and handling schedules were fixed or mixed. They were more likely to accept the long alternative when the search states were fixed-interval rather than mixed-interval schedules, and more likely to reject the long alternative when the handling states were fixed-time rather than mixed-time schedules. This pattern of results was in qualitative agreement with the predictions of the hyperbolic-decay model, which states that the value of a reinforcer is inversely related to the delay between a choice response and reinforcer delivery.