388 Frequently Asked Questions In Quantitative Finance
he only needs 1 doubloon. But how to get two votes
from the remaining Pirates 3, 2 and 1?
There are clearly several options here. And we are
going to have to think carefully about the actions of
the Pirates when faced with uncertainty.
Imagine being Pirate 2 when Pirate number 6 is allocat-
ing the gold. Suppose he gives you zero, what do you
do? You may as well vote against, because there is a
chance that on the next round you will get two doub-
loons. If Pirate 6 gives you two doubloons you should
vote in favour. Things cannot be improved on the next
round but may get worse. If given one doubloon now,
what should you do? Next round you will either get zero
or two. A tricky choice. And a possibly personal one.
But it is up to Pirate 6 to make sure you are not faced
with that tricky decision which may result in his expul-
sion from the boat.
The conclusion is that Pirate 6 should give two
doubloons to any of Pirates 3, 2 and 1. It doesn’t matter
which.
Pirate 6 Pirate 5 Pirate 4 Pirate 3 Pirate 2 Pirate 1
1000 0
1000 0 0
998011
997 0 1 2 / 0 0 / 2
995 0 1 2 / 2 / 0 2 / 0 / 2 0 / 2 / 2
On Pirate 7’s turn he will give zero to Pirate 6, one to
Pirate 5 and two to any of Pirates 4 down to 1, again it
doesn’t matter which two, they will both now vote in
his favour.
Pirate 7 Pirate 6 Pirate 5 Pirate 4 Pirate 3 Pirate 2 Pirate 1
1000 0
1000 0 0
998011
997 0 1 2 / 0 0 / 2
995 0 1 2 / 2 / 0 2 / 0 / 2 0 / 2 / 2
995 0 1 Two doubloons to any two of these four
