Modeling Myopic Decisions: Evidence for Hyperbolic Delay-Discounting within Subjects and Amounts

Abstract

Hyperbolic and exponential discounting functions were compared as models of subjects′ present valuations of delayed rewards. Previous comparisons have been limited by relying on the assumption that discounting rate is independent of reward size; we avoided this limitation by making all comparisons within reward sizes. In Experiment 1, using real rewards in a simulated auction, and in Experiment 2, using hypothetical rewards, we offered subjects five monetary rewards at six delays each and asked them to indicate the smallest amount that they would accept immediately in exchange for those rewards. Both discounting functions were then fit to the six reported amounts for each reward using nonlinear regressions. In both experiments, although both functions fit the data very well, the hyperbolic function fit better for all of the delayed rewards. Furthermore, the hyperbolic function better described the data for 20 of 21 and 14 of 18 subjects in Experiments 1 and 2, respectively.