You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How should he allocate the gold in order to maximize his share but live to enjoy it? (Hint: One pirate ends up with 98 percent of the gold.)
* Answer in the comments *
Assuming everyone acts logically and cannot negotiate:
If only 1 pirate remains, he gets all the money, thus will always vote no.
If 2 pirates remain, pirate 1 will get all the money because pirate 1 will vote no to any other deal.
If 3 pirates remain, pirate 2 will accept 1 coin because he will not get anything otherwise. Pirate 4 knows pirate 3 will vote no to any deal because by killing pirate 4, pirate 3 gets nearly all the money. If pirate 3 and pirate 1 both vote no to pirate 4, he will be killed.
Therefore, pirate 4 must vote yes to pirate 5′s suggestion and only needs to offer 2 coins to pirate 2 in order to beat pirate 3′s offer.
Therefore, pirate 5 keeps 98 coins and offers pirate 2, 2 coins. Pirate 4 and pirate 2 vote yes to pirate 5′s offer.