Hyperbolic Discounting

Hyperbolic V=A/(1+kτ) vs exponential V=A·e−δτ discounting. The preference reversal: we prefer the larger-later reward when both are far away, but switch when the smaller-sooner one becomes imminent.

k (hyperbolic) 0.30
δ (exponential) 0.20
A₁ (soon,small) 5
A₂ (late,large) 10