The Classic Pirate Problem: A Game Theory Puzzle
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- čas přidán 15. 08. 2021
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The Dread Pirate Nash and his four crewmates have just discovered ten gold coins. Per pirate tradition, it is up to Nash to propose a division. If the crew does not vote to accept it, he will have to walk the plank. Will Nash be able to survive? And if so, can he keep any gold in the process?
There is a good chance you have seen this one before. Apologies if so! However, I have some original, more complicated pirate problems planned. Just needed to get this one out first before doing the more complex ones.
Pretty easy to see why being strategic and rational has become so rare.
I love this series
I really like these generalisable but hard to generalise puzzles, like the pirate puzzle, the bomb the squares puzzle and the trolley problem. By hard to generalise I mean that there are many variables at work, for example in the trolley problem there is the number of options you have, the number of options your opponent has and the payoffs for each choice of options.
The generalisation is in the way the problem is solved, and not the specific solution.
The classic pirate problem? More like “The perfect cure for boredom!” Thanks for uploading another video on a very stimulating game theory puzzle!
I was thinking about a simple variation of this problem: what if, instead of a designed heir, the new captain would be selected at random? I did not think enough about it, but as a rough esteem I think that votes would become much more expensive (maybe as much as half of all the coins?)
Interesting idea! I will add it to the list of things to do.
With 3 people you have to pay 1 voter 6 coins to overcome the expected value of voting no, which would be 5 + the value of being captain. The EV of going down to 3 people is 3.3, and the EV of getting down to 4 is 2.5. So with that logic I believe you have to pay the 2 voters 3 coins each in the 5 person situation. The value of being captain only comes into play in the 3 person situation since coins you get are, EV-wise, the same either way.
Why would they sell themselves this cheap if they could potentially make an favourable offer themselves? How do you account for bluffing?
There's no bluffing, since each pirate knows exactly what each other pirate will do at each step. If Pirates 3 and 5 vote no to this resolution (a 8-0-1-0-1 split), the next resolution passes with a X-9-0-1-0 split and they each get less gold than the original proposal.
@@Math.Bandit but how is next step/backwards induction even possible if they all know What the nash pirate will do? As soon as the other pirates knows that the other pirates knows wouldnt they then bluff? The primary condition of staying alive would be satisfied, in the moment.
@@user-fs5fc1vv7y Since all the facts are on the table you cannot bluff. This is like a poker game where all the cards are face up.
there is no room for negotiations as there would be in real life. Instead, the ballet is cast as a simple yes or no question. If negotiations were in place, we would meet somewhere in the middle of cost-value between the pirates, as explained in other videos by spaniel.
but isn't such backwards deduction very questionable, because of chaos theory? If you have to conduct backwards deduction over long periods of time, chances are high for intervening variables, like a royal armada, which takes out all pirates. In hindsight of that, every pirate should have in incentive to accept the first offer.
We have a game theoretic context here, so we are thinking that everything else is frozen in time or something like that.
@@andreizonga4611 but isn't it a bit problematic for an actor, to base her action solely on the current state.I think it would be more accurate to discuss a range of possible outcomes.
@@EarnestBunbury This is a Game Theory exercise. It is not meant as a substitute for the study of socially dynamic interactions. It is not necessary to discuss the range of possibilities of outcomes given the constraints of the exercise.
That would be similar to when introductory lessons for physics, eg trajectory equations, it is advised to neglect frictional forces and assume that the exercise is happening in a perfect vacuum, despite the fact that perfect vacuums do not exist.
Another example would be asking why a math textbook farmer is trying to buy another watermelon despite him already owning hundreds and suggesting that he should put up his watermelon growing capacity available for speculative market trading instead.
well, I actually have a better technique.
We should remove a person from south east as you said, but since the demon wont know my move, he probably think that I chose the south route since I removed human from south west. Now, rather than pulling the lever for south route, I am going to choose the norther one bcz I am pretty sure the demon chose east the moment I removed someoene from south west. Although its a double edge sword if he chose the east one, but we all know he wants to increase casualities, thus he will choose the west one if I gave him a fake sign that I will choose the south one. Following this strategy, we can make sure there is only 2 casualities.
Just think about it and I would like to know if there is a flaw in this strategy.
I think you commented this on the wrong video.