Expert-Level Pirate Problem: A Game Theory Puzzle
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- เผยแพร่เมื่อ 22 ก.ย. 2021
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It's the classic pirate problem with a twist. The Dread Pirate Nash has just discovered a trove of gold coins. Per pirate tradition, he must now divide them by proposing a division among his seven crewmates. If at least half accept, the proposal is implemented. Otherwise, the Dread Pirate Nash must walk the plank, and the second-ranking pirate must repeat the process.
What's the fewest number of gold coins that still assures the Dread Pirate Nash's survival?
This was a really cool "Aha!" moment when I realized the significance of the pirates who will act when there are 2^n pirates remaining.
Yep, the generalization to n pirates gets really weird because you start needed progressively (and exponentially) larger coalitions for the captain to survive.
Pirate problem? More like "perfect perspective"! Thanks for taking us inside the minds of the pirates. And just when I thought that three coins was the minimum, you expertly levelled my supposition!
I think the real realization is when you think about how Dread Pirate Nash became commander on the fleet. If there were any number of pirates between 9 and 15, all of them would have been voted off and thrown into death.
Can’t wait for the Dread Pirate Nash fanfics to pop up here.
The 0 coin solution was very interesting
Very nice puzzle, thank you
Interestingly, while offering 0 coins to each pirate is the best that Nash can do, it is not the only Nash Equilibrium. There are more. Do you agree? I can explain how if there is a need.
I'm not sure what you mean. Are you referring to a technical point about the equilibrium concept? It is true that there are multiple Nash equilibria for this type of game, but what I describe in the video is the unique subgame perfect equilibrium.
Hey, I was wondering if you have any videos regarding game theory for 3 players. Expressed in like a cubic matrix
I have that on my whiteboard as a thing to eventually do, but I have no short-term plans for it.
This was good, I’d give you all my gold coins
Fortunately, it's possible for you to not have any, give me none, and still remain captain. :)
@@Gametheory101 Well played!
So clever！
What if there were only 1 gold coin? Pirate 2 could vote no, give the coin to pirate 8, survive and get a promotion.
so Nash survives if he has 0 or more than 2 coins
can he still survive if there is 1 or 2 coins?
Two is fine, one is no good. I will leave the backward induction for that up to you. :)