Discounting of delayed rewards: Models of individual choice

The present paper addresses the question of the form of the mathematical relation between the time until a delayed reward and its present value. Data are presented from an experiment in which subjects chose between hypothetical amounts of money available either immediately or after a delay (Green, Fry, & Myerson, 1994). Analyses of the behavior of individual young adults demonstrated that temporal discounting is better described by hyperbola-like functions than by exponential decay functions. For most individuals, the parameter that determines the rate of discounting varied inversely with amount. Raising the denominator of the discounting function to a power resulted in better descriptions of the data from most subjects. Two possible derivations of the temporal discounting function are proposed, a repeated choice model and an expected value model. These provide theoretical interpretations for amount-dependent discounting but amount-independent exponent parameters.