A review of the relationship between schedule of reinforcement, response rate, and choice suggests that certain unifying concepts from economics can contribute to a more complete science of behavior. Four points are made: 1) a behavioral experiment is an economic system and its characteristics—open or closed—can strongly determine the results; 2) reinforcers can be distinguished by a functional property called elasticity; 3) reinforcers may interact as complements as well as substitutes; 4) no simple choice rule, such as strict matching, can account for all choice behavior.

/pdf/economic-concepts-for-the-analysis-of-behavior-2jck8dw9z3.pdf

Economic concepts for the analysis of behavior

Almost all of 103 sets of data from 23 different studies of choice conformed closely to the equation: log (B(1)/B(2)) = a log (r(1)/r(2)) + log b, where B(1) and B(2) are either numbers of responses or times spent at Alternatives 1 and 2, r(1) and r(2) are the rates of reinforcement obtained from Alternatives 1 and 2, and a and b are empirical constants. Although the matching relation requires the slope a to equal 1.0, the best-fitting values of a frequently deviated from this. For B(1) and B(2) measured as numbers of responses, a tended to fall short of 1.0 (undermatching). For B(1) and B(2) measured as times, a fell to both sides of 1.0, with the largest mode at about 1.0. Those experiments that produced values of a for both responses and time revealed only a rough correspondence between the two values; a was often noticeably larger for time. Statistical techniques for assessing significance of a deviation of a from 1.0 suggested that values of a between .90 and 1.11 can be considered good approximations to matching. Of the two experimenters who contributed the most data, one generally found undermatching, while the other generally found matching. The difference in results probably arises from differences in procedure. The procedural variations that lead to undermatching appear to be those that produce (a) asymmetrical pausing that favors the poorer alternative; (b) systematic temporal variation in preference that favors the poorer alternative; and (c) patterns of responding that involve changing over between alternatives or brief bouts at the alternatives.

Matching, undermatching, and overmatching in studies of choice.

Maximization theory, which is borrowed from economics, provides techniques for predicing the behavior of animals - including humans. A theoretical behavioral space is constructed in which each point represents a given combination of various behavioral alternatives. With two alternatives - behavior A and behavior B - each point within the space represents a certain amount of time spent performing behavior A and a certain amount of time spent performing behavior B. A particular environmental situation can be described as a constraint on available points (a circumscribed area) within the space. Maximization theory assumes that animals always choose the available point with the highest numerical value. The task of maximization theory is to assign to points in the behavioral space values that remain constant across various environmental situations; as those situations change, the point actually chosen is always the one with the highest assigned value.Maximization theory is an alternative to reinforcement theory as a description of steady-state behavior. Situations to which reinforcement theory has been directly applied (such as reinforcement of rats pressing levers and pigeons pecking keys in Skinner boxes) and situations to which reinforcement theory has occasionally been extended (such as human economic behavior and human self-control) can be described by maximization theory. This approach views behavior as a quantitative outcome of the interaction of the putative instrumental response, the reinforcer, and the other activities available in the situation. It provides new insight into these situations and, because it takes context into account, has greater predictive power than reinforcement theory.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0140525X00009407

Maximization theory in behavioral psychology

Foraging and reinforcement schedules in the pigeon: Optimal and non-optimal aspects of choice

CHAPTER 5 – Melioration and Behavioral Allocation1

The extant data for pigeons' performance on concurrent variable-interval schedules were examined in detail. Least-squares lines relating relative pecks and time to the corresponding relative reinforcements were obtained for four studies. The between-study group slopes for time and pecks and five of seven within-study group slopes from individual studies were less than 1.00. This suggested the generality that pigeons respond less to the richer reinforcement schedule than predicted by matching. For pecks, a nonparametric test for distribution of points also supported this concept of undermatching (to the richer reinforcement schedule). In addition, using mean squared error as the criterion, a cubic curve fit the peck proportion data better than any line or other polynomial. This indicates that the relation between peck and reinforcement proportions may be nonlinear.

Undermatching: a reappraisal of performance on concurrent variable-interval schedules of reinforcement.

Each of five pigeons was exposed to two or more durations of access to mixed grains on two-link, chained, interval schedules in which both links were identical fixed-interval or variable-interval schedules. Response rates were an increasing function of reinforcer duration for both initial and terminal links. For both types of interval schedules, initial-link response rates were more sensitive to reinforcer duration than were terminal-link response rates. The present results, together with prior ones, suggest that chaining and choice procedures are each sufficient for demonstrating substantial sensitivity of responding to changes in reinforcer duration.

David L. Myers

Papers

Undermatching: a reappraisal of performance on concurrent variable-interval schedules of reinforcement.

Effects of reinforcer duration on responding in two-link chained interval schedules.