Herrnstein's hyperbolic matching equation and behavioral pharmacology: review and critique

Behavioral pharmacologists have enlisted Herrnstein's (1970) hyperbolic matching equation to understand the behavioral effects of drugs. Herrnstein's hyperbola describes the relation between absolute response rate and reinforcement rate. The equation has two fitted parameters. The parameter k represents the asymptotic response rate, and the parameter r(e) represents the reinforcement rate necessary to obtain half the asymptotic response rate. According to one interpretation of the equation, changes in k should reflect changes in response or motoric variables, and changes in r(e) should reflect changes in reinforcer or motivational variables, or changes in reinforcement from sources extraneous to the instrumental response. We review research that has applied Herrnstein's equation to distinguish the motoric from the motivational effects of drugs, and to identify additional independent variables responsible for drug effects, such as extraneous reinforcement. The validity of inferences about drug effects depends on the consistency of how k and r(e) respond to environmental manipulations: k should change only with response or motoric variables, and r(e) should change with reinforcer or motivational variables and with the rate of extraneous reinforcement. Empirical tests of these predictions, however, have produced inconsistent results. The review suggests that Herrnstein's theory has not fulfilled its promise of identifying the behavioral mechanisms of drug action. Modifications to the equation, known as bias and sensitivity, may explain some of these inconsistent results, and the modified equation may have utility in behavioral pharmacology.