Two rewards sit ahead in time: A = $50, arriving after a short delay, and B = $100, arriving later still. As "now" advances (the elapsed-time slider, or drag directly on the middle timeline panel), both delays shrink by the same amount. How much each reward is worth right now depends on the discounting model:
Hyperbolic (Mazur, 1987): V(t) = Amount / (1 + k·t)
Exponential (classic economic model): V(t) = Amount · e^(−k·t)
Exponential discounting is time-consistent: the ratio VA/VB never changes as elapsed time increases, because both delays shrink by the identical amount — whichever reward you prefer at a distance, you still prefer up close. Hyperbolic discounting is not: it falls off steeply for short delays and gently for long ones, so as the smaller reward's remaining delay approaches zero its subjective value shoots up disproportionately, which can flip the preference from "wait for B" to "take A now" — the textbook mechanism behind present bias, procrastination and impulsive choice reversal.
This 2D build renders the same two-model mechanism as three linked panels instead of a 3D scene: a discount-curve chart (value vs. raw delay), a draggable decision timeline (remaining delay for each reward, to scale), and a k-vs-elapsed reversal map that shades every combination of discount rate and elapsed time by which reward currently wins — so you can see the whole reversal region at once, not just the single point your sliders are at.
- Hyperbolic / Exponential — switch the discounting function applied to both rewards; the reversal map recolors instantly (exponential's map is a single flat boundary, hyperbolic's bows because the crossover point depends on k).
- k — steepness of the discount; higher k devalues delayed rewards faster. A horizontal cursor line tracks it on the reversal map.
- Delay to A at rest / Extra delay to B — sets the two reward horizons before any time has elapsed; changes the curve chart's time axis and the map's geometry.
- Elapsed time — slides the vantage point ("now") forward; drag it, press Auto-advance, or drag directly on the timeline panel to watch the markers slide toward the origin and see whether the preferred reward changes. A vertical cursor line tracks it on the reversal map.
Real-world relevance: this is the mechanism cited for why people sign up for a gym membership starting "next month" but skip today's session, why savers under-contribute to retirement accounts, and why commitment devices (locking in a choice while it is still far away) can out-perform willpower alone.