(Not sure if this is the right forum for this)
There’s a gang of murderous pirates. They are motivated as follows:
Highest priority: They want to live. Above all else, each pirate will never take an action that results in his dying.
Next priority: They are greedy. They will act so as to maximize the amount of gold they end up with
Third priority: They are bloodthirsty. They will act so as to kill as many of their fellow pirates as possible.
They are also (of course) brilliant logicians with perfect calculating skills, and are all aware of all of the above about each other. They are also totally untrustworthy, and know that none will ever keep his word if it means getting less gold.
Let’s assume that there are P pirates, numbered 1 … P (with 1 being the most senior and P the most junior), and they have G indivisible and interchangeable gold pieces.
They are going to divide up the Gold pieces in the following fashion: The juniormost pirate will propose an allocation scheme (ie, “1 gets 7 gold, 2 gets 5 gold, 3 gets 0 gold, etc.”). Then they will vote on it, each pirate (including the juniormost) voting yea or nay. If a majority vote yay, the scheme is accepted, everyone walks off with their gold, and no one dies. If there is a tie, or if a majority vote nay, the juniormost pirate is killed, and the next juniormost now proposes a scheme, etc.
What happens for various choices of G and P. For instance, G=100 and P=10?
(Note: I have actually left undefined a subtle but important characteristic of pirate behavior so, assuming my understanding of this problem is correct, which is not necessarily a safe assumption, your first response should be “But Max, what happens when X”)