There are five pirates who must split up their booty of 100 gold coins. Each of the pirates is rational, intelligent, greedy and murderous. They have agreed upon a system to divide up the treasure, as follows:
The five pirates, A, B, C, D, and E, are ranked in order of authority, with A being more powerful than B, B more powerful than C, and so on. To decide the division of coins, starting with A, each pirate will make a proposal of how to divide up the coins. Each of the living pirates votes on the proposal, and if half or more of the pirates vote yes, then the proposal is accepted, the treasure is shared according to those terms, and the process is over. If the proposal does not receive enough votes, then the pirate who proposed it is made to walk the plank and dies, at which point the pirate next in authority makes a new proposal, to be voted on in the same way.
Because the pirates are all rational, intelligent, and greedy, each will think carefully about how to maximize gold for himself. Because they are all murderous, each pirate would prefer to murder one or more of his fellows, as long as it does not reduce his own share of gold.
You are pirate A, the first pirate to make a proposal. Given what you know, what distribution of gold should you propose, to maximize treasure for yourself and stay out of Davy Jones’ locker?See Answer
If only pirates D and E are still living, then D is in an excellent position. D may propose that D get 100 gold coins and E get zero. In the vote, D will vote yes and E will vote no. Because half of the living pirates voted yes, the proposal is accepted.
If only C, D, and E are still living, then all of them, including C, will be thinking of the potential scenario above. In order to save his skin, C only needs to propose a distribution that gives E more than he would have otherwise, i.e. more than zero. So C can propose that C get 99 coins, D get zero, and E get one. C and E will vote yes, so that will be the distribution.
If only B, C, D, and E are still living, then all will be aware of the potential scenarios above. In order to avoid becoming food for the sharks, B need only get one other pirate on board, and the clear choice is D, who would get zero otherwise. So B need only propose that B get 99 coins, C get zero, D get one, and E get zero. B and D will vote yes, and the proposal will be successful.
So, you, as pirate A about to make the first proposal, are aware of all of the above potentialities and you know the other pirates are too. Following the same logic, you merely need to propose that you get 98 coins, B gets zero, C gets 1, D gets zero, and E gets 1.