# Hyperbolic Discounting

Hyperbolic discounting holds that people usually prefers the smaller and sooner payoffs than larger and later payoffs. They prefer the smaller payoffs that are immediate but if the same payoffs are distant, then people prefer the larger payoffs. Interestingly, even if the time lag between the smaller and larger payoffs is same as before the preference of people does not change.

The following mathematical equation gives the functional explanation for hyperbolic discounting:
f(D) = 1/ (1 + kD)

Here,

f(D) holds the value for the discount factor, which multiplies the value of the reward.
D refers to the delay in the reward.
k is the parameter that governs the discounting degree

When describing hyperbolic discounting, the degree of discounting plays a vital role. The discounting value of monetary rewards changes with respect to the various age groups due to the changing rate of k. The value of the parameter k is dependant on a number of factors like the age, species being observed, experience and most importantly the time that is needed to consume the reward.

The quasi-hyperbolic discount function is the further enhancement over the hyperbolic discount theory and this approximates the hyperbolic discount function. The mathematical relation for the quasi-hyperbolic discount function is:
f(0) = 1, and f(D) = β * δD,

Here,
β and δ are constants ranging between 0 and 1;
D refers to the delay in the reward,
f(D) refers to the discount factor.

The condition f(0) = 1 states that rewards that are taken at present time are not discounted. The Quasi-hyperbolic discounting theory of time preferences is also called as beta-delta or present-biased preferences.

Very recently the concept of hyperbolic discounting is being used to study the borrowing on credit cards, saving for retirement and procrastination. But the hyperbolic discounting is mostly used to explain the concept of addiction. The hyperbolic discounting theory is also applicable to explain the real-life examples of self-control. In order to explain the behavior of drug-addicted people the hyperbolic discounting theory proves to be of great use. 