A few weeks ago, we
blogged about the paper, An Option Value
Problem from Seinfeld, by Avinash Dixit (Princeton University). From this
weekend’s Dear Economist (Tim Harford) column:
I
have inherited six bottles of excellent wine, which I plan to consume, over
time, on special occasions. But how do I know when to open a bottle when I
don’t know what occasions lie ahead? I don’t want to use up all the bottles
within a few months on mediocre occasions, but neither do I still want to be
hoarding them until I die.
George
Stevens
Dear George,
This is known as the “spongeworthiness”
problem, after an episode of Seinfeld in which the contraceptive sponge is
taken off the market. The character Elaine Benes stocks up with several hundred
sponges, but then faces the same problem you do: how to decide whether a man is
“spongeworthy”.
This is an option-value problem: every
sponge or bottle consumed is one that cannot be used later. It has been solved
by Avinash Dixit, a renowned game theorist and former president of the American
Economic Association. (For some reason, Professor Dixit waited to finish his
term of office before publishing his research on spongeworthiness.) Unless you
are absurdly patient, you should open them more quickly than you might think.
Assuming you are patient enough to wait
for a gain of 5 per cent a year – but not more – and if you have one possibly
special occasion per month, Dixit calculates that you should open a bottle if
you expect an occasion in the top 21 per cent of all possible occasions. As the
number of bottles remaining shrinks, raise your standards. The last bottle
should be consumed on an occasion in the top 9 per cent.
Of course, there is always the chance
that an occasion is so special that you are tempted to open another bottle.
Dixit’s analysis allows for this. After all, Elaine once told a lover that he
couldn’t have a second bout: “Sorry, I can’t afford two of them.”