Physical and cognitive effort discounting across different reward magnitudes: Tests of discounting models

Abstract

The effort required to obtain a rewarding outcome is an important factor in decision-making. Describing the reward devaluation by increasing effort intensity is substantial to understanding human preferences, because every action and choice that we make is in itself effortful. To investigate how reward valuation is affected by physical and cognitive effort, we compared mathematical discounting functions derived from research on discounting. Seven discounting models were tested across three different reward magnitudes. To test the models, data were collected from a total of 114 participants recruited from the general population. For one-parameter models (hyperbolic, exponential, and parabolic), the data were explained best by the exponential model as given by a percentage of explained variance. However, after introducing an additional parameter, data obtained in the cognitive and physical effort conditions were best described by the power function model. Further analysis, using the second order Akaike and Bayesian Information Criteria, which account for model complexity, allowed us to identify the best model among all tested. We found that the power function best described the data, which corresponds to conventional analyses based on the R2 measure. This supports the conclusion that the function best describing reward devaluation by physical and cognitive effort is a concave one and is different from those that describe delay or probability discounting. In addition, consistent magnitude effects were observed that correspond to those in delay discounting research.

Fig 1. Empirical indifference points obtained in cognitive (left panel) and physical (right panel) effort discounting, with curves fitted corresponding to the one-parameter exponential model in three different reward magnitudes.

Fig 2. Empirical indifference points obtained in cognitive (left panel) and physical (right panel) effort discounting, with curves fitted corresponding to the two-parameter power function model in three different reward magnitudes.

Fig 3. Theoretical account for the effects of varying parameter s and l values: Holding constant the value of s with low and high l values (left panel), and holding constant the value of l with low and high s values (right panel).