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

J. Dallery, P. L. Soto

Research output: Contribution to journalReview articlepeer-review

17 Scopus citations


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 re 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 re respond to environmental manipulations: k should change only with response or motoric variables, and re 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.

Original languageEnglish (US)
Pages (from-to)443-459
Number of pages17
JournalBehavioural Pharmacology
Issue number7
StatePublished - Nov 2004
Externally publishedYes


  • Behavioral mechanisms
  • Behavioral pharmacology
  • Herrnstein's hyperbola
  • Human
  • Matching theory
  • Rat
  • Rate-dependency

ASJC Scopus subject areas

  • Pharmacology
  • Psychiatry and Mental health


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