Absolute Hours Discount Hyperbolically
Paying exorbitant airport prices for earbuds is a uniquely painful experience. (True story: @dave once bought earbuds at an airport that we had previously sold for 3X the Meh price.)
How can this excruciating feeling be avoided? One possible solution: Buy these crazy cheap Maximo Earbuds and stow one in your carry-on bag as a permanent feature. You’ll never pay Hudson News earbud-famine prices again.
One reason you might not do that: Hyperbolic discounting.
Hyperbolic discounting, in a nutshell (that economics nerds will excoriate us for), is the human tendency to want a smaller reward soon than a larger reward in the future. It explains irrational behaviors like eating cake now (small reward) when you know you would feel better later if you didn’t (larger reward).
The Grasshopper, in other words, represents the hyperbolic discounter to the Ant’s rational economic actor.
In the case of these earbuds, the value of having them as backups at some future date might seem lower than keeping $8 in your pocket right now. But when you (eventually) find yourself shelling out $25 for them at the airport, you’ll kick your past self and its stupid hyperbolic discounting.
However, humans may hyperbolically discount because of uncertain risks. You might die next week. Or you might never forget your ear buds again.
Suppose that the probability for the reward to be available after time t is, for known hazard rate λ
but the rate is unknown to the decision maker. If the prior probability distribution of λ is
then, the decision maker will expect that the probability of the reward after time t is
which is exactly the hyperbolic discount rate.
OK, we might have cribbed that last part from Wikipedia, but the rest was original[citation needed], we swear[dubious].
