Relative sensitivity to reinforcer amount and delay in a self-control choice situation.

Rats were exposed to concurrent-chains schedules in which a single variable-interval schedule arranged entry into one of two terminal-link delay periods (fixed-interval schedules). The shorter delay ended with the delivery of a single food pellet; the longer day ended with a larger number of food pellets (two under some conditions and six under others). In Experiment 1, the terminal-link delays were selected so that under all conditions the ratio of delays would exactly equal the ratio of the number of pellets. But the absolute duration of the delays differed across conditions. In one condition, for example, rats chose between one pellet delayed 5 s and six pellets delayed 30 s; in another condition rats chose between one pellet delayed 10 s and six pellets delayed 60 s. The generalized matching law predicts indifference between the two alternatives, assuming that the sensitivity parameters for amount and delay of reinforcement are equal. The rats' choices were, in fact, close to indifference except when the choice was between one pellet delayed 5 s and six pellets delayed 30 s. That deviation from indifference suggests that the sensitivities to amount and delay differ from each other depending on the durations of the delays. In Experiment 2, rats chose between one pellet following a 5-s delay and six pellets following a delay that was systematically increased over sessions to find a point of indifference. Indifference was achieved when the delay to the six pellets was approximately 55 s. These results are consistent with the possibility that the relative sensitivities to amount and delay differ as a function of the delays.     

Choice between rewards differing in amount and delay: Toward a choice model of self control

A concurrent-chain procedure was used to study pigeons' choices between rewards differing in both amount and delay. The shorter delay terminated with a 2-second access to grain whereas the longer delay terminated with a 6-second access to grain. The ratio of the delays was constant within a given condition while their absolute values were varied. Over conditions, ratios of 6:1, 3:1, and 3:2 were studied. As the absolute values of the delays to reinforcement increased, preference for the longer-delayed but larger reward decreased under both the 6:1 and 3:1 ratios, but increased under the 3:2 ratio. These results are inconsistent with choice models predicting no change in preference when the ratios of delays and amounts are held constant. In addition, the change in preference under the 3:1 ratio is inconsistent with a simple multiplicative interaction of the trade off between reinforcer amount and delay, and suggests that delay is a more potent determinant of choice than is amount. These results have implications for models that view choice between small immediate rewards and large but delayed rewards as underlying the behavior commonly called self control.     

Effects of intertrial reinforcers on self-control choice.

In three experiments, pigeons chose between a small amount of food delivered after a short delay and a larger amount delivered after a longer delay. A discrete-trial adjusting-delay procedure was used to estimate indifference points--pairs of delay-amount combinations that were chosen about equally often. In Experiment 1, when additional reinforcers were available during intertrial intervals on a variable-interval schedule, preference for the smaller, more immediate reinforcer increased. Experiment 2 found that this shift in preference occurred partly because the variable-interval schedule started sooner after the smaller, more immediate reinforcer, but there was still a small shift in preference when the durations and temporal locations of the variable-interval schedules were identical for both alternatives. Experiment 3 found greater increases in preference for the smaller, more immediate reinforcer with a variable-interval 15-s schedule than with a variable-interval 90-s schedule. The results were generally consistent with a model that states that the impact of any event that follows a choice response declines according to a hyperbolic function with increasing time since the moment of choice.     

Operant hoarding: a new paradigm for the study of self-control.

In the first of four experiments, rats were exposed to a modified multiple continuous reinforcement-extinction schedule during 15-min daily sessions. In one condition (saves condition) with the cuelight on, a single lever press produced a food pellet, briefly extinguished the cuelight, and started a clock. Saves (additional lever presses with interresponse times less than 1 s) produced an additional food pellet, briefly extinguished the cuelight, and restarted the interresponse time clock. The cuelight was extinguished 1 s after the last lever press and remained off during a 10-s period of extinction, during which no food pellets were delivered. In the other condition (savings account condition), the contingencies were the same except that the cuelight was extinguished and was not reilluminated after the initial lever press, and the delivery of all food pellets in the reinforcement component was delayed until the onset of extinction. In both conditions, rats made saves, but mean saves (total saves divided by the number of reinforcement components) were slightly reduced in the savings account condition. In Experiment 2, using six equally spaced 15-min sessions per day on alternate days, saves were either followed immediately with food and brief cuelight offset (saves condition) or were not reinforced at all. Mean saves were much greater when saves were reinforced. In Experiment 3, during 5-min daily sessions, saves earned a single pellet (savings account condition) or a number of pellets equal to the ordinal number of the lever press (interest condition). Rats made fewer mean saves, with little change in the food rate, when saves earned interest. In Experiment 4, the rats earned all their food in the operant situation during 24 daily 5-min sessions, these separated by 55-min intersession intervals during which no food was available; otherwise, the conditions were the same as in Experiment 3. In Experiment 4, the shift to interest for saves led to an increase in mean daily mean saves (total daily mean saves divided by the number of daily sessions) as well as to an increase in the number of food pellets delivered in each session. The results are discussed in terms of self-control and behavioral economics.     

Humans' sensitivity to variation in reinforcer amount: Effects of the method of reinforcer delivery

Two experiments examined human subjects' sensitivity to variation in reinforcer amount under different methods of reinforcer delivery. Subjects chose between schedules varying in terms of amount and/or delay of reinforcement, the reinforcer being points exchangeable for money. In Experiment 1, reinforcer amount was manipulated by varying the monetary value of the points across conditions while the number of seconds of access to a consummatory response remained constant. Choice was strongly sensitive to reinforcer amount and indicative of self-control, as in previous experiments. In Experiment 2, reinforcer amount was manipulated by automatically delivering different numbers of points during the amount period, and the consummatory response was eliminated. Sensitivity to variation in reinforcer amount was significantly lower than in Experiment 1. Furthermore, the subjects in Experiment 2 exhibited significantly less self-control than did the subjects in Experiment 1. Humans' sensitivity to variation in reinforcer amount appears to be affected by factors that enhance the discrimi-nability of the consequences of responding.     

DYNAMICS OF CHOICE: RELATIVE RATE AND AMOUNT AFFECT LOCAL PREFERENCE AT THREE DIFFERENT TIME SCALES

To examine extended control over local choice, the present study investigated preference in transition as food‐rate ratio provided by two levers changed across seven components within daily sessions, and food‐amount ratio changed across phases. Phase 1 arranged a food‐amount ratio of 4:1 (i.e., the left lever delivered four pellets and the right lever one pellet); Phase 2 reversed the food‐amount ratio to 1:4, and in Phase 3 the food‐amount ratio was 3:2. At a relatively extended time scale, preference was described well by a linear relation between log response ratio and log rate ratio (the generalized matching law). A small amount of carryover occurred from one rate ratio to the next but disappeared after four food deliveries. Estimates of sensitivity to food‐amount ratio were around 1.0 and were independent of rate ratio. Analysis across food deliveries within rate‐ratio components showed that the effect of a small amount was diminished by the presence of a large amount—that is, when a larger amount was present in the situation (three or four pellets), the value of a small amount (one or two pellets) became paltry. More local analysis of visits to the levers between food deliveries showed that postfood visits following a large amount were disproportionately longer than following a small amount. Continuing food deliveries from the same source tended to make visits less dependent on relative amount, but a discontinuation (i.e., food from the other lever) reinstated dependence on relative amount. Analysis at a still smaller time scale revealed preference pulses following food deliveries that confirmed the tendency toward dependence on absolute amount with continuing deliveries, and toward dependence on relative amount following discontinuations. A mathematical model based on a linear‐operator equation accounts for many of the results. The larger and longer preference following a switch to a larger amount is consistent with the idea that local preference depends on relatively extended variables even on short time scales.     

Response rate correlates with indifference points in a delay‐discounting procedure

To study how effort affects reward value, we replicated Fortes, Vasconcelos and Machado's (2015) study using an adjusting‐delay task. Nine pigeons chose between a standard alternative that gave access to 4 s of food, after a 10 s delay, and an adjusting‐delay alternative that gave access to 12 s of food after a delay that changed dynamically with the pigeons' choices, decreasing when they preferred the standard alternative, and increasing when they preferred the adjusting alternative. The delay value at which preference stabilized defined the indifference point, a measure of reward value. To manipulate effort across phases, we varied the response rate required during the delay of the standard alternative. Results showed that a) the indifference point increased in the higher‐response‐rate phases, suggesting that reward value decreased with effort, and b) in the higher‐response‐rate phases, response rate in the standard alternative was linearly related to the indifference point. We advance several conceptions of how effort may change perceived delay or amount and thereby affect reward value.     

DISCOUNTING OF DELAYED FOOD REWARDS IN PIGEONS AND RATS: IS THERE A MAGNITUDE EFFECT?

Temporal discounting refers to the decrease in the present, subjective value of a reward as the time to its receipt increases. Results from humans have shown that a hyperbola-like function describes the form of the discounting function when choices involve hypothetical monetary rewards. In addition, magnitude effects have been reported in which smaller reward amounts are discounted more steeply than larger amounts. The present research examines the cross-species generality of these findings using real rewards, namely food pellets, with both pigeons and rats. As with humans, an adjusting amount procedure was used to estimate the amount of immediate reward judged equal in value to a delayed reward. Different amounts of delayed food rewards (ranging from 5 to 32 pellets in pigeons and from 5 to 20 pellets in rats) were studied at delays varying from 1 s to 32 s. A simple hyperbola, similar to the hyperbola-like mathematical function that describes the discounting of hypothetical monetary rewards in humans, described the discounting of food rewards in both pigeons and rats. These results extend the generality of the mathematical model of discounting. Rates of discounting delayed food rewards were higher for pigeons than for rats. Unlike humans, however, neither pigeons nor rats showed a reliable magnitude effect: Rate of discounting did not vary systematically as a function of the amount of the delayed reward.     

Effects of pre-trial response requirements on self-control choices by rats and pigeons

Parallel experiments with rats and pigeons examined whether the size of a pre-trial ratio requirement would affect choices in a self-control situation. In different conditions, either 1 response or 40 responses were required before each trial. In the first half of each experiment, an adjusting-ratio schedule was used, in which subjects could choose a fixed-ratio schedule leading to a small reinforcer, or an adjusting-ratio schedule leading to a larger reinforcer. The size of the adjusting ratio requirement was increased and decreased over trials based on the subject's responses, in order to estimate an indifference point-a ratio at which the two alternatives were chosen about equally often. The second half of each experiment used an adjusting-delay procedure-fixed and adjusting delays to the small and large reinforcers were used instead of ratio requirements. In some conditions, particularly with the reinforcer delays, the rats had consistently longer adjusting delays with the larger pre-trial ratios, reflecting a greater tendency to choose the larger, delayed reinforcer when more responding was required to reach the choice point. No consistent effects of the pre-trial ratio were found for the pigeons in any of the conditions. These results may indicate that rats are more sensitive to the long-term reinforcement rates of the two alternatives, or they may result from a shallower temporal discounting rate for rats than for pigeons, a difference that has been observed in previous studies.