Hyperbolic Discounting — Temporal Preference Reversal

Exponential discounting D(t)=e^(−δt) is time-consistent but empirically wrong. Humans discount hyperbolically: D(t)=1/(1+kt), which causes preference reversals — you prefer $110 next week over $100 now, but also prefer $100 today over $110 tomorrow. This seemingly irrational pattern arises because hyperbolic curves for two rewards can cross as time passes, flipping the preferred choice.

0.30
0.10
50
100
1
10