Preference for mixed versus constant delays of reinforcement: Effect of probability of the short, mixed delay

Preference for mixed versus constant delays of reinforcement was studied with a concurrent-chain procedure. Lever pressing by rats in concurrently available variable-interval 60-second initial links occasionally produced mutually exclusive terminal-link reinforcement delays. A constant delay of reinforcement (either 15 seconds or 30 seconds) composed one terminal link and mixed delays (.2 second and twice the value of the constant delay) were arranged in the other terminal link. The proportion of .2-second delays in the mixed-delay terminal link took on values of 0, .1, .25, .5, .75, .9, and 1.0 over experimental conditions. Based on relative rates of responding in the initial links, preference for the mixed delays was a negatively accelerated function of the proportion of short, mixed delays. Three of five rats preferred the mixed delays to the constant delays when the proportion of short, mixed delays was .1 or higher, and all five rats preferred the mixed delays when the proportion of short, mixed delays was .25 or higher. Neither Squires and Fantino's (1971) delay-reduction model of choice nor a model based on the harmonic mean reinforcement delay provided a close estimate of choice proportions over the range of short-delay proportions studied. The delay-reduction model underestimated choice for the mixed delays at low and intermediate proportions of short delays, and the harmonic-mean-delay model overestimated choice for the mixed delays at intermediate and high proportions of short delays.     

Response rate, latency, and resistance to change

Pigeons were trained on a multiple variable-interval/variable-interval schedule with pacing contingencies that generated high response rates in one component and low response rates in the other. Timeout periods separated the schedule components. During resistance-to-change tests, response-independent food was presented during the timeout periods, and the duration of that food presentation was varied among test sessions. Response rates in the schedule components decreased and latencies to the first response increased as a function of the duration of food presentations during the timeout. Both dependent measures changed about the same amount relative to their own baseline levels. The conclusions are that baseline response rates controlled by pacing contingencies are equally resistant to change, given equal reinforcement densities, and latency is a sensitive measure of resistance to change.     

Hill-climbing by pigeons

Pigeons were exposed to two types of concurrent operant-reinforcement schedules in order to determine what choice rules determine behavior on these schedules. In the first set of experiments, concurrent variable-interval, variable-interval schedules, key-peck responses to either of two alternative schedules produced food reinforcement after a random time interval. The frequency of food-reinforcement availability for the two schedules was varied over different ranges for different birds. In the second series of experiments, concurrent variable-ratio, variable-interval schedules, key-peck responses to one schedule produced food reinforcement after a random time interval, whereas food reinforcement occurred for an alternative schedule only after a random number of responses. Results from both experiments showed that pigeons consistently follow a behavioral strategy in which the alternative schedule chosen at any time is the one which offers the highest momentary reinforcement probability (momentary maximizing). The quality of momentary maximizing was somewhat higher and more consistent when both alternative reinforcement schedules were time-based than when one schedule was time-based and the alternative response-count based. Previous attempts to provide evidence for the existence of momentary maximizing were shown to be based upon faulty assumptions about the behavior implied by momentary maximizing and resultant inappropriate measures of behavior.     

Concurrent schedules: Spatial separation of response alternatives

Four pigeons were exposed to independent concurrent variable-interval 20-second variable-interval 60-second schedules of reinforcement. A transparent partition was inserted midway between the two response keys. The length of the partition was systematically manipulated. Increasing partition length produced a decrease in changeover rate in Experiment 1. Over-matching was observed with a partition length of 20 centimeters. In Experiment 2 a four-second limited hold was added to the schedules. Increasing partition length produced a decrease in changeover rate that exceeded the decrease observed in Experiment 1. This manipulation produced nearly exclusive choice of the variable-interval 20-second component. The present results, together with results obtained in related research, suggest that deviation from matching is a function of procedural variables that determine the consequences of a changeover response.     

A simple BASIC program to generate values for variable-interval schedules of reinforcement

A BASIC program to generate values for variable-interval (VI) schedules of reinforcement is presented. A VI schedule should provide access to reinforcement with a constant probability over a time horizon. If the values in a VI schedule are calculated from an arithmetic progression, the probability of reinforcement is positively correlated with the time since the last reinforcer was delivered. Fleshler and Hoffman (1962) developed an iterative equation to calculate VI schedule values so that the probability of reinforcement remains constant. This easy-to-use program generates VI schedule values according to the Fleshler and Hoffman equation, randomizes the values, and saves the values in ASCII to a disk file.     

Tolerance to and residual effects of cocaine in squirrel monkeys depend on reinforcement-schedule parameter.

Lever pressing by 4 squirrel monkeys was maintained under a three-component multiple fixed-ratio schedule of food presentation; components differed with respect to ratio size. For each monkey, acute administration of cocaine (0.03 to 1.3 mg/kg, i.m.) produced dose-dependent decreases in overall response rate in each component. During repeated daily administration of 1.0 mg/kg of cocaine, tolerance developed to the rate-decreasing effects under each of the ratio contingencies, but developed to a greater extent and was evident in earlier parts of sessions for performance under the smaller ratios. Response rates of 2 monkeys increased above nondrug control levels despite the putative reinforcer not being consumed during the session. When saline or a smaller dose of cocaine was substituted for 1.0 mg/kg, response rates often were suppressed below nondrug control-level responding. This suppressive effect was observed in each monkey and was more likely to be observed and/or to be of greater magnitude in large-ratio components for 3 of the 4 monkeys. When saline was administered chronically at the end of the chronic-drug phase, response rates remained suppressed in the large-ratio component for 2 of the monkeys. There was, therefore, a schedule-dependent dissociation between behavioral tolerance and the residual effects: Tolerance was greater when small ratios were arranged, whereas the residual effects were more pronounced when larger ratios were arranged.     

Choice as a function of local versus molar reinforcement contingencies.

Rats were trained on a discrete-trial probability learning task. In Experiment 1, the molar reinforcement probabilities for the two response alternatives were equal, and the local contingencies of reinforcement differentially reinforced a win-stay, lose-shift response pattern. The win-stay portion was learned substantially more easily and appeared from the outset of training, suggesting that its occurrence did not depend upon discrimination of the local contingencies but rather only upon simple strengthening effects of individual reinforcements. Control by both types of local contingencies decreased with increases in the intertrial interval, although some control remained with intertrial intervals as long as 30 s. In Experiment 2, the local contingencies always favored win-shift and lose-shift response patterns but were asymmetrical for the two responses, causing the molar reinforcement rates for the two responses to differ. Some learning of the alternation pattern occurred with short intertrial intervals, although win-stay behavior occurred for some subjects. The local reinforcement contingencies were discriminated poorly with longer intertrial intervals. In the absence of control by the local contingencies, choice proportion was determined by the molar contingencies, as indicated by high exponent values for the generalized matching law with long intertrial intervals, and lower values with short intertrial intervals. The results show that when molar contingencies of reinforcement and local contingencies are in opposition, both may have independent roles. Control by molar contingencies cannot generally be explained by local contingencies.     

Subjective probability and delay.

Human subjects indicated their preference between a hypothetical $1,000 reward available with various probabilities or delays and a certain reward of variable amount available immediately. The function relating the amount of the certain-immediate reward subjectively equivalent to the delayed $1,000 reward had the same general shape (hyperbolic) as the function found by Mazur (1987) to describe pigeons' delay discounting. The function relating the certain-immediate amount of money subjectively equivalent to the probabilistic $1,000 reward was also hyperbolic, provided that the stated probability was transformed to odds against winning. In a second experiment, when human subjects chose between a delayed $1,000 reward and a probabilistic $1,000 reward, delay was proportional to the same odds-against transformation of the probability to which it was subjectively equivalent.     

Choice, changeover, and travel: A quantitative model

Six pigeons were trained on concurrent variable-interval schedules in which responding on fixed-interval schedules was required to give access to the alternate schedule. Responding on the concurrent schedules was not allowed, after changing over had commenced, until the changeover schedule had been completed. In Parts 1 to 3 of the experiment, the changeover fixed-interval schedules were equal and were 0 s, 10 s, and 20 s, respectively. In each part, the relative frequency of reinforcement obtained on the concurrent schedules was varied over at least five conditions. In Part 4, the concurrent schedules were equal, and one changeover fixed-interval schedule was twice the other. Under these conditions, the absolute sizes of the changeover schedules were varied. Increasing the changeover requirement from 0 s to 10 s (Parts 1 and 2) resulted in increases in the sensitivity of behavior allocation to reinforcers obtained, but no further increase was obtained when the changeover schedules were increased to 20 s (Part 3). In Part 4, performance was biased towards the concurrent schedule that took less time to enter. These results are consistent with a subtractive punishment model of travel in which the degree of punishment is measured by the number of reinforcers apparently lost from a schedule when the subject changes to that schedule. Absolute times spent on the main keys could be accurately described by a previous model of changeover performance.     

Violations of stochastic transitivity on concurrent chains: Implications for theories of choice

The concurrent-chains procedure has been used to measure how choice depends on various aspects of reinforcement, such as its delay and its magnitude. Navarick and Fantino (1972, 1974, 1975) have found that choice in this procedure can violate the condition of stochastic transitivity that is required if a unidimensional scale for reinforcements is to be possible. It is shown in this paper that two simple unidimensional models of choice on concurrent chains can produce violations of stochastic transitivity. It is argued that such violations may result from the complex contingencies of the concurrent-chains procedure.