Second-order schedules of token reinforcement with pigeons: implications for unit price

Four pigeons were exposed to second-order schedules of token reinforcement, with stimulus lights serving as token reinforcers. Tokens were earned according to a fixed-ratio (token-production) schedule, with the opportunity to exchange tokens for food (exchange period) occurring after a fixed number had been produced (exchange-production ratio). The token-production and exchange-production ratios were manipulated systematically across conditions. Response rates varied inversely with the token-production ratio at each exchange-production ratio. Response rates also varied inversely with the exchange-production ratio at each token-production ratio, particularly at the higher token-production ratios. At higher token-production and exchange-production ratios, response rates increased in token-production segments closer to exchange periods and food. Some conditions were conducted in a closed economy, in which the pigeons earned all their daily ration of food within the session. Relative to comparable open-economy conditions, response rates in the closed economy were less affected by changes in token-production ratio, resulting in higher levels of food intake and body weight. Some of the results are consistent with the economic concept of unit price, a cost-benefit ratio comprised of responses per unit of food delivery, but most are well accounted for by a consideration of the number of responses required to produce exchange periods, without regard to the amount of reinforcement available during those exchange periods.     

Second-order schedules of token reinforcement with pigeons: effects of fixed- and variable-ratio exchange schedules

Pigeons' key pecks produced food under second-order schedules of token reinforcement, with light-emitting diodes serving as token reinforcers. In Experiment 1, tokens were earned according to a fixed-ratio 50 schedule and were exchanged for food according to either fixed-ratio or variable-ratio exchange schedules, with schedule type varied across conditions. In Experiment 2, schedule type was varied within sessions using a multiple schedule. In one component, tokens were earned according to a fixed-ratio 50 schedule and exchanged according to a variable-ratio schedule. In the other component, tokens were earned according to a variable-ratio 50 schedule and exchanged according to a fixed-ratio schedule. In both experiments, the number of responses per exchange was varied parametrically across conditions, ranging from 50 to 400 responses. Response rates decreased systematically with increases in the fixed-ratio exchange schedules, but were much less affected by changes in the variable-ratio exchange schedules. Response rates were consistently higher under variable-ratio exchange schedules than tinder comparable fixed-ratio exchange schedules, especially at higher exchange ratios. These response-rate differences were due both to greater pre-ratio pausing and to lower local rates tinder the fixed-ratio exchange schedules. Local response rates increased with proximity to food under the higher fixed-ratio exchange schedules, indicative of discriminative control by the tokens.     

REINFORCER ACCUMULATION IN A TOKEN-REINFORCEMENT CONTEXT WITH PIGEONS

Four pigeons were exposed to a token-reinforcement procedure with stimulus lights serving as tokens. Responses on one key (the token-production key) produced tokens that could be exchanged for food during an exchange period. Exchange periods could be produced by satisfying a ratio requirement on a second key (the exchange-production key). The exchange-production key was available any time after one token had been produced, permitting up to 12 tokens to accumulate prior to exchange. Token accumulation, measured in terms of both frequency (percent cycles with accumulation) and magnitude (mean number of tokens accumulated), decreased as the token-production ratio increased from 1 to 10 across conditions (with exchange-production ratio held constant), and increased as the exchange-production ratio increased from 1 to 250 across conditions (with token-production ratio held constant). When tokens were removed, accumulation decreased markedly compared to conditions with tokens and the same schedules. These data show that token accumulation is an orderly function of token-production and exchange-production schedules, and they are broadly consistent with a unit-price model based on local and global responses per reinforcer.     

Effects of reinforcement context on choice

Two experiments investigated the effects of successive reinforcement contexts on choice. In the first, concurrent variable-interval schedules of primary reinforcement operated during the initial links of concurrent chains. The rate of this reinforcement arranged by the concurrent schedules was decreased across conditions: When it was higher than the terminal-link rate, preference for the higher frequency initial-link schedule increased relative to baseline. (During baseline, a standard concurrent-schedule procedure was in effect). When the initial-link reinforcement rate was lower than the terminal-link rate, preference converged toward indifference. In the second experiment, a chain schedule was available on a third key while a concurrent schedule was in effect on the side keys. When the terminal link of the chain schedule was produced, the side keys became inoperative. Availability of the chain schedule did not affect choice between the concurrent schedules. These results show that only when successive reinforcement contexts are produced by choice responding do those successive contexts affect choice in concurrent schedules.     

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.     

Development and maintenance of choice in a dynamic environment

Four pigeons were exposed to a concurrent procedure similar to that used by Davison, Baum, and colleagues (e.g., Davison & Baum, 2000, 2006) in which seven components were arranged in a mixed schedule, and each programmed a different left∶right reinforcer ratio (1∶27, 1∶9, 1∶3, 1∶1, 3∶1, 9∶1, 27∶1). Components within each session were presented randomly, lasted for 10 reinforcers each, and were separated by 10-s blackouts. These conditions were in effect for 100 sessions. When data were aggregated over Sessions 16-50, the present results were similar to those reported by Davison, Baum, and colleagues: (a) preference adjusted rapidly (i.e., sensitivity to reinforcement increased) within components; (b) preference for a given alternative increased with successive reinforcers delivered via that alternative (continuations), but was substantially attenuated following a reinforcer on the other alternative (a discontinuation); and (c) food deliveries produced preference pulses (immediate, local, increases in preference for the just-reinforced alternative). The same analyses were conducted across 10-session blocks for Sessions 1-100. In general, the basic structure of choice revealed by analyses of data from Sessions 16-50 was preserved at a smaller level of aggregation (10 sessions), and it developed rapidly (within the first 10 sessions). Some characteristics of choice, however, changed systematically across sessions. For example, effects of successive reinforcers within a component tended to increase across sessions, as did the magnitude and length of the preference pulses. Thus, models of choice under these conditions may need to take into account variations in behavior allocation that are not captured completely when data are aggregated over large numbers of sessions.     

Variation, repetition, and choice

Experiment 1 investigated the controlling properties of variability contingencies on choice between repeated and variable responding. Pigeons were exposed to concurrent-chains schedules with two alternatives. In the REPEAT alternative, reinforcers in the terminal link depended on a single sequence of four responses. In the VARY alternative, a response sequence in the terminal link was reinforced only if it differed from the n previous sequences (lag criterion). The REPEAT contingency generated low, constant levels of sequence variation whereas the VARY contingency produced levels of sequence variation that increased with the lag criterion. Preference for the REPEAT alternative tended to increase directly with the degree of variation required for reinforcement. Experiment 2 examined the potential confounding effects in Experiment 1 of immediacy of reinforcement by yoking the interreinforcer intervals in the REPEAT alternative to those in the VARY alternative. Again, preference for REPEAT was a function of the lag criterion. Choice between varying and repeating behavior is discussed with respect to obtained behavioral variability, probability of reinforcement, delay of reinforcement, and switching within a sequence.     

The influence of "preparedness" on autoshaping, schedule performance, and choice.

Two groups of experimentally naive pigeons were exposed to an autoshaping procedure in which the response key was mounted on the wall (the conventional location) or on the floor of the chamber. In two experiments, subjects readily responded to the wall key, but floor-key subjects required shaping. A subsequent experiment compared performance of wall- and floor-key groups on an ascending series of fixed-ratio schedule values, resistance to extinction, differential reinforcement of other behavior, and reversal of key assignment. Each experiment was followed by several sessions of fixed-ratio training; the performance of the wall- and floor-key groups was almost identical throughout. In the final experiment, a fixed-ratio requirement could be completed on either or both keys. Birds initially chose the key on which they had responded during the preceding (reversal of key assignment) experiment. However, within a few sessions both groups showed almost exclusive preference for the floor key. Preference for a key located on the floor may follow from the fact that pigeons are ground feeders and may thus be more "prepared" to peck the floor than to peck a wall. However, autoshaping, under the conditions prevailing here, occurred much more readily to the wall key, suggesting that pecking a vertical surface is more highly prepared. Difficulties in determining relative preparedness seem moot, however, given the lack of between-group differences in the intervening experiments. It is thus unlikely that schedule performances critically depend upon the specific operant response involved.     

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.     

Choice between fixed-interval schedules: Graded versus step-like choice functions

Pigeons chose between two fixed-interval schedules of food reinforcement. A single peck on one of two lighted keys started the fixed-interval schedule correlated with that key. The schedule had to be completed before the next choice opportunity. The durations of the fixed intervals were varied over conditions from 15 s to 40 s. To maximize the rate of reinforcement, the pigeons had to choose exclusively the shorter of the two schedules. Nevertheless, choice was not all-or-none. Instead, relative choice, and the rates of producing the fixed intervals, varied in a graded fashion with the disparity between the two schedules. Choice ratios under this procedure (single response to choose) were highly sensitive to the ratios of the fixed-interval schedules.     

Substitution effects in a generalized token economy with pigeons

Pigeons made repeated choices between earning and exchanging reinforcer‐specific tokens (green tokens exchangeable for food, red tokens exchangeable for water) and reinforcer‐general tokens (white tokens exchangeable for food or water) in a closed token economy. Food and green food tokens could be earned on one panel; water and red water tokens could be earned on a second panel; white generalized tokens could be earned on either panel. Responses on one key produced tokens according to a fixed‐ratio schedule, whereas responses on a second key produced exchange periods, during which all previously earned tokens could be exchanged for the appropriate commodity. Most conditions were conducted in a closed economy, and pigeons distributed their token allocation in ways that permitted food and water consumption. When the price of all tokens was equal and low, most pigeons preferred the generalized tokens. When token‐production prices were manipulated, pigeons reduced production of the tokens that increased in price while increasing production of the generalized tokens that remained at a fixed price. The latter is consistent with a substitution effect: Generalized tokens increased and were exchanged for the more expensive reinforcer. When food and water were made freely available outside the session, token production and exchange was sharply reduced but was not eliminated, even in conditions when it no longer produced tokens. The results join with other recent data in showing sustained generalized functions of token reinforcers, and demonstrate the utility of token‐economic methods for assessing demand for and substitution among multiple commodities in a laboratory context.     

Molar optimization versus delayed reinforcement as explanations of choice between fixed-ratio and progressive-ratio schedules.

In a discrete-trials procedure, pigeons chose between a fixed-ratio 81 schedule and a progressive-ratio schedule by making a single peck at the key correlated with one or the other of these schedules. The response requirement on the progressive-ratio schedule began at 1 and increased by 10 each time the progressive-ratio schedule was chosen. Each time the fixed-ratio schedule was chosen, the requirement on the progressive-ratio schedule was reset to 1 response. In conditions where there was no intertrial interval, subjects chose the progressive-ratio schedule for an average of about five consecutive trials (during which the response requirement increased to 41), and then chose the fixed-ratio schedule. This ratio was larger than that predicted by an optimality analysis that assumes that subjects respond in a pattern that minimizes the response-reinforcer ratio or one that assumes that subjects respond in a pattern that maximizes the overall rate of reinforcement. In conditions with a 25-s or 50-s intertrial interval, subjects chose the progressive-ratio schedule for an average of about eight consecutive trials before choosing the fixed-ratio schedule. This change in performance with the addition of an intertrial interval was also not predicted by an optimality analysis. On the other hand, the results were consistent with the theory that choice is determined by the delays to the reinforcers delivered on the present trial and on subsequent trials.     

Nonstable concurrent choice in pigeons

Six pigeons were trained on concurrent variable-interval schedules in which the arranged reinforcer ratios changed from session to session according to a 31-step pseudorandom binary sequence. This procedure allows a quantitative analysis of the degree to which performance in an experimental session is affected by conditions in previous sessions. Two experiments were carried out. In each, the size of the reinforcer ratios arranged between the two concurrent schedules was varied between 31-step conditions. In Experiment 1, the concurrent schedules were arranged independently, and in Experiment 2 they were arranged nonindependently. An extended form of the generalized matching law described the relative contribution of past and present events to present-session behavior. Total performance in sessions was mostly determined by the reinforcer ratio in that session and partially by reinforcers that had been obtained in previous sessions. However, the initial exposure to the random sequence produced a lower sensitivity to current-session reinforcers but no difference in overall sensitivity to reinforcement. There was no evidence that the size of the reinforcer ratios available on the concurrent schedules affected either overall sensitivity to reinforcement or the sensitivity to reinforcement in the current session. There was also no evidence of any different performance between independent and nonindependent scheduling. Because of these invariances, this experiment validates the use of the pseudorandom sequence for the fast determination of sensitivity to reinforcement.     

Response summation to a compound stimulus in a context of choice

Key pecks by two groups of pigeons were reinforced on concurrent schedules. For group Ē, pecks were reinforced during either a visual or an auditory stimulus; for group E, an additional, extinction component was available, during which both visual and auditory stimuli were absent. After training, both groups were given a compound test to measure preference among four stimuli, the three used in training plus a compound of the visual and auditory stimulus. Group E showed preference for the compound, emitting more pecks and spending more time in this stimulus than in other stimuli. Group Ē showed no preference between the compound and visual stimulus, nor between the auditory stimulus and the absence of both stimuli, but preferred the former pair over the latter pair of stimuli.     

Choice with a fixed requirement for food, and the generality of the matching relation

Pigeons were trained on choice procedures in which responses on each of two keys were reinforced probabilistically, but only after a schedule requirement had been met. Under one arrangement, a fixed-interval choice procedure was used in which responses were not reinforced until the interval was over; then a response on one key would be reinforced, with the effective key changing irregularly from interval to interval. Under a second, fixed-ratio choice procedure, responses on either key counted towards completion of the ratio and then, once the ratio had been completed, a response on the probabilistically selected key would produce food. In one experiment, the schedule requirements were varied for both fixed-interval and fixed-ratio schedules. In the second experiment, relative reinforcement rate was varied. And in a third experiment, the duration of an intertrial interval separating choices was varied. The results for 11 pigeons across all three experiments indicate that there were often large deviations between relative response rates and relative reinforcement rates. Overall performance measures were characterized by a great deal of variability across conditions. More detailed measures of choice across the schedule requirement were also quite variable across conditions. In spite of this variability, performance was consistent across conditions in its efficiency of producing food. The absence of matching of behavior allocation to reinforcement rate indicates an important difference between the present procedures and other choice procedures; that difference raises questions about the specific conditions that lead to matching as an outcome.     

Time and rate measures in choice transitions

Three experiments with pigeons studied the relation between time and rate measures of behavior under conditions of changing preference. Experiment 1 studied a concurrent chain schedule with random-interval initial links and fixed-interval terminal links; Experiment 2 studied a multiple chained random-interval fixed-interval schedule; and Experiment 3 studied simple concurrent random-interval random-interval schedules. In Experiment 1, and to a lesser extent in the other two experiments, session-average initial-link wait-time differences were linearly related to session-average response-rate differences. In Experiment 1, and to a lesser extent in Experiment 3, ratios of session-average initial-link wait times and response rates were related by a power function. The weaker relations between wait and response measures in Experiment 2 appear to be due to the absence of competition between responses. In Experiments 1 and 2, initial-link changes lagged behind terminal-link changes. These findings may have implications for the relations between fixed- and variable-interval procedures and suggest that more attention should be paid to temporal measures in studies of free-operant choice.     

Preference between variable-ratio and fixed-ratio schedules: local and extended relations.

Although it has repeatedly been demonstrated that pigeons, as well as other species, will often choose a variable schedule of reinforcement over an equivalent (or even richer) fixed schedule, the exact nature of that controlling relation has yet to be fully assessed. In this study pigeons were given repeated choices between concurrently available fixed-ratio and variable-ratio schedules. The fixed-ratio requirement (30 responses) was constant throughout the experiment, whereas the distribution of individual ratios making up the variable-ratio schedule changed across phases: The smallest and largest of these components were varied gradually, with the mean variable-ratio requirement constant at 60 responses. The birds' choices of the variable-ratio schedule tracked the size of the smallest variable-ratio component. A minimum variable-ratio component at or near 1 produced strong preference for the variable-ratio schedule, whereas increases in the minimum variable-ratio component resulted in reduced preference for the variable-ratio schedule. The birds' behavior was qualitatively consistent with Mazur's (1984) hyperbolic model of delayed reinforcement and could be described as approximate maximizing with respect to reinforcement value.