Within-subject comparison of real and hypothetical money rewards in delay discounting.

Six adults without disabilities made choices between small money now or larger money later. Some choices paid real dollars. Other choices paid pretend dollars. The team compared how fast people "discounted" future rewards in both conditions.

Each person served as their own control. Sessions ran in a lab. The researchers fit two math models to see which curve tracked the choices better.

For five of six people, discount rates looked the same with real or hypothetical cash. One person valued real money less steeply, but the difference was tiny.

A simple hyperbolic curve fit every person's data better than the older exponential curve. Hypothetical rewards gave the same picture as costly real ones.

Malagodi et al. (1975) also ran single-case lab studies with tangible pay-offs. They showed that pigeons adjusted pecking when token-to-food ratios changed. Both papers confirm that single-case lab methods can reveal clear economic preferences.

Cicerone (1976) used the same one-person-at-a-time design to show that reinforcement rate, not sensitivity, drives bias in duration tasks. Horner-Johnson et al. (2002) mirror that logic: the pay-off type (real vs. fake) did not drive bias; delay did.

Bellon-Harn et al. (2020) warn that different rating tools can tag the very same single-case study as strong or weak. Their caution applies here: always check model fit, not just face value, when you interpret discount curves.

You can skip paying participants real cash when you study delay discounting. Hypothetical choices give the same curve, saving money and ethics paperwork. Use the hyperbolic model to describe the data; it wins almost every time. If you run preference assessments or self-control training, this gives you a cheaper, faster way to map how clients devalue delayed rewards.