Effects of reinforcer rate and reinforcer quality on time allocation: Extensions of matching theory to educational settings

We examined how 3 special education students allocated their responding across two concurrently available tasks associated with unequal rates and equal versus unequal qualities of reinforcement. The students completed math problems from two alternative sets on concurrent variable-interval (VI) 30-s VI 120-s schedules of reinforcement. During the equal-quality reinforcer condition, high-quality (nickels) and low-quality items ("program money" in the school's token economy) were alternated across sessions as the reinforcer for both sets of problems. During the unequal-quality reinforcer condition, the low-quality reinforcer was used for the set of problems on the VI 30-s schedule, and the high-quality reinforcer was used for the set of problems on the VI 120-s schedule. Equal- and unequal-quality reinforcer conditions were alternated using a reversal design. Results showed that sensitivity to the features of the VI reinforcement schedules developed only after the reinforcement intervals were signaled through countdown timers. Thereafter, when reinforcer quality was equal, the time allocated to concurrent response alternatives was approximately proportional to obtained reinforcement, as predicted by the matching law. However the matching relation was disrupted when, as occurs in most natural choice situations, the quality of the reinforcers differed across the response options.     

Self-control and choice in humans: Effects of video game playing as a positive reinforcer

Participants chose between reinforcement schedules differing in delay of reinforcement (interval between a choice response and onset of a video game) and/or amount of reinforcement (duration of access to the game). Experiment 1 showed that immediate reinforcement was preferred to delayed reinforcement with amount of reinforcement held constant, and a large reinforcer was preferred to a small reinforcer when both were obtainable immediately. Imposing a delay before the large reinforcer produced a preference for the immediate, small reinforcer in 40% of participants. This suggested a limited degree of “impulsivity.” In Experiment 2, unequal delays were extended by equal intervals, the amounts being kept equal. Preference for the shorter delay decreased, an effect that presumably makes possible the “preference reversal” phenomenon in studies of self-control. Overall, the results demonstrate that video game playing can produce useful, systematic data when used as a positive reinforcer for choice behavior in humans.     

Stimulus Equivalence: Effects Of A Default-response Option On Emergence Of Untrained Stimulus Relations

Human subjects were exposed to a concurrent-chains schedule in which reinforcer amounts, delays, or both were varied in the terminal links, and consummatory responses were required to receive points that were later exchangeable for money. Two independent variable-interval 30-s schedules were in effect during the initial links, and delay periods were defined by fixed-time schedules. In Experiment 1, subjects were exposed to three different pairs of reinforcer amounts and delays, and sensitivity to reinforcer amount and delay was determined based on the generalized matching law. The relative responding (choice) of most subjects was more sensitive to reinforcer amount than to reinforcer delay. In Experiment 2, subjects chose between immediate smaller reinforcers and delayed larger reinforcers in five conditions with and without timeout periods that followed a shorter delay, in which reinforcer amounts and delays were combined to make different predictions based on local reinforcement density (i.e., points per delay) or overall reinforcement density (i.e., points per total time). In most conditions, subjects' choices were qualitatively in accord with the predictions from the overall reinforcement density calculated by the ratio of reinforcer amount and total time. Therefore, the overall reinforcement density appears to influence the preference of humans in the present self-control choice situation.     

Sensitivity to reinforcer duration in a self-control procedure

In a concurrent-chains procedure, pigeons' responses on left and right keys were followed by reinforcers of different durations at different delays following the choice responses. Three pairs of reinforcer delays were arranged in each session, and reinforcer durations were varied over conditions. In Experiment 1 reinforcer delays were unequal, and in Experiment 2 reinforcer delays were equal. In Experiment 1 preference reversal was demonstrated in that an immediate short reinforcer was chosen more frequently than a longer reinforcer delayed 6 s from the choice, whereas the longer reinforcer was chosen more frequently when delays to both reinforcers were lengthened. In both experiments, choice responding was more sensitive to variations in reinforcer duration at overall longer reinforcer delays than at overall shorter reinforcer delays, independently of whether fixed-interval or variable-interval schedules were arranged in the choice phase. We concluded that preference reversal results from a change in sensitivity of choice responding to ratios of reinforcer duration as the delays to both reinforcers are lengthened.     

Sensitivity to relative reinforcer rate in concurrent schedules: independence from relative and absolute reinforcer duration

Twelve pigeons responded on two keys under concurrent variable-interval (VI) schedules. Over several series of conditions, relative and absolute magnitudes of reinforcement were varied. Within each series, relative rate of reinforcement was varied and sensitivity of behavior ratios to reinforcer-rate ratios was assessed. When responding at both alternatives was maintained by equal-sized small reinforcers, sensitivity to variation in reinforcer-rate ratios was the same as when large reinforcers were used. This result was observed when the overall rate of reinforcement was constant over conditions, and also in another series of concurrent schedules in which one schedule was kept constant at VI ached 120 s. Similarly, reinforcer magnitude did not affect the rate at which response allocation approached asymptote within a condition. When reinforcer magnitudes differred between the two responses and reinforcer-rate ratios were varied, sensitivity of behavior allocation was unaffected although response bias favored the schedule that arranged the larger reinforcers. Analysis of absolute response rates ratio sensitivity to reinforcement occurrred on the two keys showed that this invariance of response despite changes in reinforcement interaction that were observed in absolute response rates on the constant VI 120-s schedule. Response rate on the constant VI 120-s schedule was inversely related to reinforcer rate on the varied key and the strength of this relation depended on the relative magnitude of reinforcers arranged on varied key. Independence of sensitivity to reinforcer-rate ratios from relative and absolute reinforcer magnitude is consistent with the relativity and independence assumtions of the matching law.     

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.     

USING A SELF-CONTROL TRAINING PROCEDURE TO INCREASE APPROPRIATE BEHAVIOR

The present study evaluated a technique for teaching self-control and increasing desirable behaviors among adults with developmental disabilities. Results showed that when participants were initially given the choice between an immediate smaller reinforcer and a larger delayed reinforcer, all participants repeatedly chose the smaller reinforcer. Concurrent fixed-duration/progressive-duration reinforcement schedules then were introduced in which initially both the smaller and larger reinforcers were available immediately. Thereafter, progressively increasing delays were introduced for the schedule associated with the larger reinforcer only. When initial short-duration requirements for access to the larger reinforcer were gradually increased, participants repeatedly selected the larger reinforcer, thereby demonstrating increased self-control.     

Choice between single and multiple delayed reinforcers.

Pigeons chose between alternatives that differed in the number of reinforcers and in the delay to each reinforcer. A peck on a red key produced the same consequences on every trial within a condition, but between conditions the number of reinforcers varied from one to three and the reinforcer delays varied between 5 s and 30 s. A peck on a green key produced a delay of adjustable duration and then a single reinforcer. The green-key delay was increased or decreased many times per session, depending on a subject's previous choices, which permitted estimation of an indifference point, or a delay at which a subject chose each alternative about equally often. The indifference points decreased systematically with more red-key reinforcers and with shorter red-key delays. The results did not support the suggestion of Moore (1979) that multiple delayed reinforcers have no effect on preference unless they are closely grouped. The results were well described in quantitative detail by a simple model stating that each of a series of reinforcers increases preference, but that a reinforcer's effect is inversely related to its delay. The success of this model, which considers only delay of reinforcement, suggested that the overall rate of reinforcement for each alternative had no effect on choice between those alternatives.     

EFFECTS OF PROBLEM DIFFICULTY AND REINFORCER QUALITY ON TIME ALLOCATED TO CONCURRENT ARITHMETIC PROBLEMS

Students with learning difficulties participated in two studies that analyzed the effects of problem difficulty and reinforcer quality upon time allocated to two sets of arithmetic problems reinforced according to a concurrent variable-interval 30-s variable-interval 120-s schedule. In Study 1, high- and low-difficulty arithmetic problems were systematically combined with rich and lean concurrent schedules (nickels used as reinforcers) across conditions using a single-subject design. The pairing of the high-difficulty problems with the richer schedule failed to offset time allocated to that alternative. Study 2 investigated the interactive effects of problem difficulty and reinforcer quality (nickels vs. program money) upon time allocation to arithmetic problems maintained by the concurrent schedules of reinforcement. Unlike problem difficulty, the pairing of the lesser quality reinforcer (program money) with the richer schedule reduced the time allocated to that alternative. The magnitude of this effect was greatest when combined with the low-difficulty problems. These studies have important implications for a matching law analysis of asymmetrical reinforcement variables that influence time allocation.     

Zebrafish choice behavior is sensitive to reinforcer rate,immediacy, and magnitude ratios

Behavioral flexibility has, in part, been defined by choice behavior changing as a function of changes in reinforcer payoffs. We examined whether the generalized matching law quantitatively described changes in choice behavior in zebrafish when relative reinforcer rates, delays/immediacy, and magnitudes changed between two alternatives across conditions. Choice was sensitive to each of the three reinforcer properties. Sensitivity estimates to changes in relative reinforcer rates were greater when 2 variable-interval schedules were arranged independently between alternatives (Experiment 1a) than when a single schedule pseudorandomly arranged reinforcers between alternatives (Experiment 1b). Sensitivity estimates for changes in relative reinforcer immediacy (Experiment 2) and magnitude (Experiment 3) were similar but lower than estimates for reinforcer rates. These differences in sensitivity estimates are consistent with studies examining other species, suggesting flexibility in zebrafish choice behavior in the face of changes in payoff as described by the generalized matching law.     

Assessment of impulsivity and the development of self-control in students with attention deficit hyperactivity disorder.

We examined a combined approach of manipulating reinforcer dimensions and delay fading to promote the development of self‐control with 3 students diagnosed with attention deficit hyperactivity disorder. First, we administered a brief computer‐based assessment to determine the relative influence of reinforcer rate (R), reinforcer quality (Q), reinforcer immediacy (I), and effort (E) on the students' choices between concurrently presented math problems. During each session, one of these dimensions was placed in direct competition with another dimension (e.g., RvI involving math problem alternatives associated with high‐rate delayed reinforcement vs. low‐rate immediate reinforcement), with all possible pairs of dimensions presented across the six assessment conditions (RvQ, RvI, RvE, QvI, QvE, IvE). The assessment revealed that the choices of all 3 students were most influenced by immediacy of reinforcement, reflecting impulsivity. We then implemented a self‐control training procedure in which reinforcer immediacy competed with another influential dimension (RvI or QvI), and the delay associated with the higher rate or quality reinforcer alternative was progressively increased. The students allocated the majority of their time to the math problem alternatives yielding more frequent (high‐rate) or preferred (high‐quality) reinforcement despite delays of up to 24 hr. Subsequent readministration of portions of the assessment showed that self‐control transferred across untrained dimensions of reinforcement.     

A comparison of delays and ratio requirements in self-control choice.

In a discrete-trial procedure, pigeons could choose between 2-s and 6-s access to grain by making a single key peck. In Phase 1, the pigeons obtained both reinforcers by responding on fixed-ratio schedules. In Phase 2, they received both reinforcers after simple delays, arranged by fixed-time schedules, during which no responses were required. In Phase 3, the 2-s reinforcer was available through a fixed-time schedule and the 6-s reinforcer was available through a fixed-ratio schedule. In all conditions, the size of the delay or ratio leading to the 6-s reinforcer was systematically increased or decreased several times each session, permitting estimation of an "indifference point," the schedule size at which a subject chose each alternative equally often. By varying the size of the schedule for the 2-s reinforcer across conditions, several such indifference points were obtained from both fixed-time conditions and fixed-ratio conditions. The resulting "indifference curves" from fixed-time conditions and from fixed-ratio conditions were similar in shape, and they suggested that a hyperbolic equation describes the relation between ratio size and reinforcement value as well as the relation between reinforcer delay and its reinforcement value. The results from Phase 3 showed that subjects chose fixed-time schedules over fixed-ratio schedules that generated the same average times between a choice response and reinforcement.     

Negative reinforcement and choice in humans

Participants chose between reinforcement schedules differing in delay and/or duration of noise offset. In Experiment 1 it was found that (1) immediate reinforcement was preferred to delayed reinforcement when amounts (durations) of reinforcement were equal; (2) a relatively large reinforcer was preferred to a smaller one when both reinforcers were obtained immediately; and (3) preference for an immediate, small reinforcer versus a delayed, large reinforcer increased as the delay preceding the large reinforcer increased, a sign of “impulsivity”. In Experiment 2, the schedules differed in amount or delay and equal intervals were added either to the constant parameter or the varied parameter. A shift from virtually exclusive preference to indifference occurred in the latter case but not the former, a result supporting a model of self-control that assumes that the value of a schedule depends on the ratio of amount and delay, and that choice between schedules depends on the ratio of these values.     

Choice with delayed and probabilistic reinforcers: effects of variability, time between trials, and conditioned reinforcers.

In a discrete-trials procedure with pigeons, a response on a green key led to a 4-s delay (during which green houselights were lit) and then a reinforcer might or might not be delivered. A response on a red key led to a delay of adjustable duration (during which red houselights were lit) and then a certain reinforcer. The delay was adjusted so as to estimate an indifference point--a duration for which the two alternatives were equally preferred. Once the green key was chosen, a subject had to continue to respond on the green key until a reinforcer was delivered. Each response on the green key, plus the 4-s delay that followed every response, was called one "link" of the green-key schedule. Subjects showed much greater preference for the green key when the number of links before reinforcement was variable (averaging four) than when it was fixed (always exactly four). These findings are consistent with the view that probabilistic reinforcers are analogous to reinforcers delivered after variable delays. When successive links were separated by 4-s or 8-s "interlink intervals" with white houselights, preference for the probabilistic alternative decreased somewhat for 2 subjects but was unaffected for the other 2 subjects. When the interlink intervals had the same green houselights that were present during the 4-s delays, preference for the green key decreased substantially for all subjects. These results provided mixed support for the view that preference for a probabilistic reinforcer is inversely related to the duration of conditioned reinforcers that precede the delivery of food.     

Choice and number of reinforcers

Pigeons were exposed to the concurrent-chains procedure in two experiments designed to investigate the effects of unequal numbers of reinforcers on choice. In Experiment 1, the pigeons were indifferent between long and short durations of access to variable-interval schedules of equal reinforcement density, but preferred a short high-density terminal link over a longer, lower density terminal link, even though in both sets of comparisons there were many more reinforcers per cycle in the longer terminal link. In Experiment 2, the pigeons preferred five reinforcers, the first of which was available after 30 sec, over a single reinforcer available at 30 sec, but only when the local interval between successive reinforcers was short. The pigeons were indifferent when this local interval was sufficiently long. The pigeons' behavior appeared to be under the control of local terminal-link variables, such as the intervals to the first reinforcer and between successive reinforcers, and was not well described in terms of transformed delays of reinforcement or reductions in average delay to reinforcement.     

Unsignaled delay of reinforcement, relative time, and resistance to change

Two experiments with pigeons examined the effects of unsignaled, nonresetting delays of reinforcement on responding maintained by different reinforcement rates. In Experiment 1, 3-s unsignaled delays were introduced into each component of a multiple variable-interval (VI) 15-s VI 90-s VI 540-s schedule. When considered as a proportion of the preceding immediate reinforcement baseline, responding was decreased similarly for the three multiple-schedule components in both the first six and last six sessions of exposure to the delay. In addition, the relation between response rates and reinforcement rates was altered such that both parameters of the single-response version of the matching law (i.e., k and Re) were decreased. Experiment 2 examined the effects of unsignaled delays ranging from 0.5 s to 8.0 s on responding maintained by a multiple VI 20-s VI 120-s schedule of reinforcement. Response rates in both components increased with brief unsignaled delays and decreased with longer delays. As in Experiment 1, response rates as a proportion of baseline were affected similarly for the two components in both the first six and last six sessions of exposure to the delay. Unlike delays imposed between two stimulus events, the effects of delays between responses and reinforcers do not appear to be attenuated when the average time between reinforcers is longer. In addition, the disruptions produced by unsignaled delays appear to be inconsistent with the general finding that responding maintained by higher rates of reinforcement is less resistant to change.     

Determinants of pigeons' choices in token-based self-control procedures

Four pigeons were exposed to a token-based self-control procedure with stimulus lights serving as token reinforcers. Smaller-reinforcer choices produced one token immediately; larger-reinforcer choices produced three tokens following a delay. Each token could be exchanged for 2-s access to food during a signaled exchange period each trial. The main variables of interest were the exchange delays (delays from the choice to the exchange stimulus) and the food delays (also timed from the choice), which were varied separately and together across blocks of sessions. When exchange delays and food delays were shorter following smaller-reinforcer choices, strong preference for the smaller reinforcer was observed. When exchange delays and food delays were equal for both options, strong preference for the larger reinforcer was observed. When food delays were equal for both options but exchange delays were shorter for smaller-reinforcer choices, preference for the larger reinforcer generally was less extreme than under conditions in which both exchange and food delays were equal. When exchange delays were equal for both options but food delays were shorter for smaller-reinforcer choices, preference for the smaller reinforcer generally was less extreme than under conditions in which both exchange and food delays favored smaller-reinforcer choices. On the whole, the results were consistent with prior research on token-based self-control procedures in showing that choices are governed by reinforcer immediacy when exchange and food delays are unequal and by reinforcer amount when exchange and food delays are equal. Further, by decoupling the exchange delays from food delays, the results tentatively support a role for the exchange stimulus as a conditioned reinforcer.     

Examining the discriminative and strengthening effects of reinforcers in concurrent schedules

Reinforcers may increase operant responding via a response-strengthening mechanism whereby the probability of the preceding response increases, or via some discriminative process whereby the response more likely to provide subsequent reinforcement becomes, itself, more likely. We tested these two accounts. Six pigeons responded for food reinforcers in a two-alternative switching-key concurrent schedule. Within a session, equal numbers of reinforcers were arranged for responses to each alternative. Those reinforcers strictly alternated between the two alternatives in half the conditions, and were randomly allocated to the alternatives in half the conditions. We also varied, across conditions, the alternative that became available immediately after a reinforcer. Preference after a single reinforcer always favored the immediately available alternative, regardless of the local probability of a reinforcer on that alternative (0 or 1 in the strictly alternating conditions, .5 in the random conditions). Choice then reflected the local reinforcer probabilities, suggesting some discriminative properties of reinforcement. At a more extended level, successive same-alternative reinforcers from an alternative systematically shifted preference towards that alternative, regardless of which alternative was available immediately after a reinforcer. There was no similar shift when successive reinforcers came from alternating sources. These more temporally extended results may suggest a strengthening function of reinforcement, or an enhanced ability to respond appropriately to "win-stay" contingencies over "win-shift" contingencies.     

Resistance to change of responding maintained by unsignaled delays to reinforcement: a response-bout analysis

Previous experiments have shown that unsignaled delayed reinforcement decreases response rates and resistance to change. However, the effects of different delays to reinforcement on underlying response structure have not been investigated in conjunction with tests of resistance to change. In the present experiment, pigeons responded on a three-component multiple variable-interval schedule for food presented immediately, following brief (0.5 s), or following long (3 s) unsignaled delays of reinforcement. Baseline response rates were lowest in the component with the longest delay; they were about equal with immediate and briefly delayed reinforcers. Resistance to disruption by presession feeding, response-independent food during the intercomponent interval, and extinction was slightly but consistently lower as delays increased. Because log survivor functions of interresponse times (IRTs) deviated from simple modes of bout initiations and within-bout responding, an IRT-cutoff method was used to examine underlying response structure. These analyses suggested that baseline rates of initiating bouts of responding decreased as scheduled delays increased, and within-bout response rates tended to be lower in the component with immediate reinforcers. The number of responses per bout was not reliably affected by reinforcer delay, but tended to be highest with brief delays when total response rates were higher in that component. Consistent with previous findings, resistance to change of overall response rate was highly correlated with resistance to change of bout-initiation rates but not with within-bout responding. These results suggest that unsignaled delays to reinforcement affect resistance to change through changes in the probability of initiating a response bout rather than through changes in the underlying response structure.     

Token reinforcement, choice, and self-control in pigeons.

Pigeons were exposed to self-control procedures that involved illumination of light-emitting diodes (LEDs) as a form of token reinforcement. In a discrete-trials arrangement, subjects chose between one and three LEDs; each LED was exchangeable for 2-s access to food during distinct posttrial exchange periods. In Experiment 1, subjects generally preferred the immediate presentation of a single LED over the delayed presentation of three LEDs, but differences in the delay to the exchange period between the two options prevented a clear assessment of the relative influence of LED delay and exchange-period delay as determinants of choice. In Experiment 2, in which delays to the exchange period from either alternative were equal in most conditions, all subjects preferred the delayed three LEDs more often than in Experiment-1. In Experiment 3, subjects preferred the option that resulted in a greater amount of food more often if the choices also produced LEDs than if they did not. In Experiment 4, preference for the delayed three LEDs was obtained when delays to the exchange period were equal, but reversed in favor of an immediate single LED when the latter choice also resulted in quicker access to exchange periods. The overall pattern of results suggests that (a) delay to the exchange period is a more critical determinant of choice than is delay to token presentation; (b) tokens may function as conditioned reinforcers, although their discriminative properties may be responsible for the self-control that occurs under token reinforcer arrangements; and (c) previously reported differences in the self-control choices of humans and pigeons may have resulted at least in part from the procedural conventions of using token reinforcers with human subjects and food reinforcers with pigeon subjects.