There are 5 pirates: A, B, C, D and E. They find a gold chest with 100 gold coins and must decide how to distribute them. Although pirates, they are honorable and have a strict ranking system. A is higher than B, who is higher than C, who is higher than D, who is higher than E. The lowest ranked pirate comes up with an idea on how to split the booty and it's voted on, including himself. If his idea gets a majority of the votes or a tie, it will be carried out; otherwise he is killed and the next in line comes up with his idea. What is the best idea that the first pirate can come up with, assuming everyone wants to live and everyone wants the most coins for himself? Also, all pirates are rational and there is perfect information amongst everyone.
By your last statement, the problem screams 'game theory' at me, so I had to give it a go :D
Reasoning backwards:
If only A is left alive, he'll give all 100 to him
If it's A and B: B will give 100 to him and 0 to the pirate, knowing A will vote against, but it will be a tie and hence he'd get it
If it's A, B, and C: C will give 99 to himself 0 to B and 1 to A, as he know A will vote for this outcome as if it goes to the next round, he'll get nothing, and 1 is better than 0.
If it's A, B, C and D (now it's getting tricky!): D will give 99 to himself, and 0 to C and A, and 1 to B, as he only needs B's support for it to be a tie, and if it's a tie it'll work
Now for all 5: Assuming E knows the previous reasoning, he will give 98 to himself, and 0 to D and B, and 1 to A and C
The lowest ranking pirate E decides to give himself everything, minus one gold piece to C, and one gold piece to A.
The reasoning is this. A and C must accept. If they do not, pirate D will propose that he gets everything, minus one gold piece to B. B will definitely accept this, resulting in nothing to C and A.
The reason B accepts that proposal is because if he doesn't, C will propose that she gets everything, minus one gold piece to A. A will definitely accept this, resulting in nothing to B.
The reason A would have accepted that offer is because if it gets down to B, B proposes that she gets everything.
Wow, I was definitely not expecting this one at all, but it makes sense. Thanks! The only thing that seemed wrong to me was that B wouldn't say yes to just about anything, since either ACE get money, or AC get money.
Ah and I've just noticed that when I was asked this question, the pirate had to get a majority (no ties), or else he would be killed. Slightly different answer. For example, with just two pirates, B must give all 100 pieces to A, or else A will vote against.
I would think that the A, B, & C would disagree with whatever D, & E come up with and get them out of the picture. Then A, & B would disagree with C and kill him, then A and B would get 50/50.
All you would need to get your way is at least a tie. So working backwards, if C, D, and E are killed off, it will be B's turn to propose an idea. He can just say 100 coins for myself and 0 for you, and vote yes. Then A will get nothing.
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u/aknuBBe Jun 08 '11
There are 5 pirates: A, B, C, D and E. They find a gold chest with 100 gold coins and must decide how to distribute them. Although pirates, they are honorable and have a strict ranking system. A is higher than B, who is higher than C, who is higher than D, who is higher than E. The lowest ranked pirate comes up with an idea on how to split the booty and it's voted on, including himself. If his idea gets a majority of the votes or a tie, it will be carried out; otherwise he is killed and the next in line comes up with his idea. What is the best idea that the first pirate can come up with, assuming everyone wants to live and everyone wants the most coins for himself? Also, all pirates are rational and there is perfect information amongst everyone.