16. Ten Pirates and Their Gold—Ten Pirates find a buried treasure of 100 pieces of gold. The challenge is to divide the gold up in some desirable way according to some rules. The first rule is that Pirate 1 is the lead pirate. Pirate 2 is the second in charge. Pirate 3 is the third most powerful and so on. The pirates have a scheme for dividing the money. They agree that the first pirate P1, will make a proposal for how the money is to be divided. If 50% or more of the pirates agree with P1’s system then it will be put into effect. If not, then P1 will be killed and the next most powerful pirate becomes the lead pirate. Now, again with one less pirate, the process repeats. Again the new lead pirate, P2, will now suggest a new process for dividing up the gold. It will be voted on with a 50% vote needed for the leader’s suggestion to pass, and less results in the death of this pirate as well.

All the pirates are very greedy and savvy—and will vote against a proposal if they can determine that they will get more gold if a proposal fails – and hence a lead pirate is killed.

They will never vote for a proposal that will give them less gold or no gold at all. How Should the Gold be Divided among the Ten Pirates? ++