Effects of changes in response requirement and deprivation on the parameters of the matching law equation: New data and review.

Abstract

The relation between response rate and reinforcement rate is described by the matching law equation. For an experiment in which there is just one explicit source of reinforcement, the equation has two parameters. The magnitude of one is equal to the response rate asymptote; the magnitude of the other is equal to the rate of reinforcement that maintains a one-half asymptotic response rate. This report describes experimental manipulations that affect these two parameters. Rats were trained on a series of variable-interval reinforcement schedules that provided reinforcement rates ranging from about 20 to 700 reinforcements per hour. The response was a lever press, and the reinforcer was water In Experiment I, the duration of the deprivation period was varied. Response rates maintained by the lower reinforcement rates showed the largest changes, and, accordingly, the parameter that is equal to the reinforcement rate for a one-half asymptotic response rate changed. In Experiment 2, the weight of the lever was varied. Response rates changed independently of reinforcement rate, and, as a result, the parameter that is equal to the asymptotic response rate changed. In Experiment 3, manipulations from Experiments 1 and 2 were combined. The results replicated those of Experiments 1 and 2, and there was no evidence of interactions. Our interpretation is that the asymptote of the matching law equation is a measure of motor performance and that the reinforcement parameter is a measure of the efficacy of the reinforcer maintaining the response. The matching law describes the relation between measures of reinforcement, such as amount and delay, and measures of behavior, such as rate and latency. The relations are described mathematically, with the terms and operations depending on such factors as the number of reinforcement sources, whether reinforcers are available simultaneously or sequentially, and the delay from response to reinforcement . Applications have varied, and they include social psychology experiments in which the frequency of conversations was the dependent variable (Conger & Killeen, 1974) and ethological studies in which the amount of time spent foraging was the measure of interest (Houston, 1986). The most elementary matching law equation applies to a situation in which there is just one measured reinforcement source, just one measured behavior, and no delay. This equation was introduced by Herrnstein (1970), and it is written as follows: