[Yoruichi-san]

After long months of adventuring the seven seas, the Pirates return with a eighth crewman just in time to star on "Who Wants to be Pirate King" on the Grand Line Network, the new hit reality Pirate Game show. The rules are as follows:

Every round the current Captain makes a proposal on who to vote off the ship that round, which the pirates vote yes or no on. If half or more of the remaining pirates vote yes, the proposal is followed and a new round begins. If more than half of the pirates vote no, the Captain walks the plank and the next ranked pirate becomes Captain, and a new round starts.

Of course, being pirates, the Captain can influence his crewmen's votes by bribing any pirate(s) with an counting number of gold coins during any and every round. The pirate's preferences are as follows:

1) Becoming Pirate King

2) The amount of gold they leave the ship with

What is the minimum number of gold coins that the Captain Straw Hat (the current Captain) has to spend in order to become Pirate King?

[Prime]

I do not see the answer to my dilemma.

The premise for the correct system/logic is that if pirate does not follow it, he will end up worse off. In my previous post, I demonstrated clearly by example that the pirates who did not follow the purported best strategy, ended better off, and some of those who did follow ended worse.

Whereas, each pirate thinks how to maximize his own situation -- not the captain’s.