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Five pirates (of different ages) have a treasure of 100 gold coins. On the ship, they decide to split the coins using the following scheme:
- The oldest pirate proposes how to share the coins, and all pirates remaining will vote for or against it.
- If
50% or more of the pirates vote for it, then the coins will be shared
that way. Otherwise, the pirate proposing the scheme will be thrown
overboard, and the process is repeated with the pirates that remain.
Assuming
that all five pirates are intelligent, rational, greedy, and do not wish
to die, what should the oldest pirate propose to a) survive and b) maximize his profit?
Let’s call them 1 2 3 4 and 5, 1 the youngest and 5 the oldest.
Let suppose that, if they have the same amount of money when the oldest is killed or not, they decide to kill him.
If there is one person, he take all.
If there are two, 2 give all to 1, else 1 would refuse, 2 would die and 1 have all.
If there are three people: if 3 is killed 1 will have everything (look for the case of two people) so 1 will want 3 killed. To avoid beeing killed he must then buy 2, and since 2 is greedy, and even 1 coin is better than anything he could have if 3 is killed, giving one coin to 2 and taking everything else is ok for 3 to survive.
If there are four people: 4 need to buy 2 people and he can’t buy 3 who will take almost everything if 4 is killed. But it can buy 2 and 1 by giving them two and one coins, wich is better than what they would have if 4 is killed.
If there are five pirates: 5 need to buy 3 pirates, he can’t buy 4, for the same reason than 4 can’t buy 3, so he need to buy 3, 2 and 1 wich can be done giving them one, three and two coins. Pirate 5 then can have 94 coins !
Since the oldest wants to survive he has to ensure that at least two of the others will vote for his proposal; he has only one chance. He should give the two youngest pirates 1 coin each (ensure survival), and keep 98 for himself (maximize profit).
The two youngest will vote for it because if they vote against then the next two oldest will split it 50/50 and it will be approved with 50% of the vote, leaving them with nothing.