Puzzle Corner

I agree that D would likely do so. Likely enough to bet your life on it?

Linda

[Laird]

I agree that D would likely do so. Likely enough to bet your life on it?

Linda

Yes. But only if we assume that the stated conditions actually hold. Do they?

P.S. Nobody is betting their life on this.

Yes. But only if we assume that the stated conditions actually hold. Do they?

The stated conditions hold, but we may be overconfident about their completeness. For example, “each pirate wants to get as much money as possible” may include taking risks to get more money. And we may not have been informed about motivations other than bloodthirstiness or about the strength of that bloodthirstiness. I’m not talking about trickery in terms of stating the conditions. I’m talking about realizing that we make assumptions when presented with a puzzle that may not be warranted. 

Now under the rules of puzzle making, you are probably right to make those assumptions. I first heard about this puzzle in the context of using it as part of a potential employment quiz. And it seemed likely that it was meant to be a simple logic puzzle. But what if it’s a game theory puzzle and we are meant to take into account that rational agents arrive at sub-optimal results (e.g. https://www.economicsnetwork.ac.uk/showc..._prisoners and https://en.m.wikipedia.org/wiki/Ultimatum_game)?

P.S. Nobody is betting their life on this.

Well Pirates A, B, and C might be, because the experimental results of the Ultimatum game (which the Pirate game is an offshoot of) should give them pause.

Linda

[Laird]

Thanks for the additional links, Linda, but, unfortunately, I think that your attempts to marry this scenario with game theory are misplaced. The logic seems to me to be inexorable given the stated conditions, and nothing you have said has convinced me otherwise. It was fun considering that it might have been otherwise though, so I appreciate your raising this possibility.

I want to address, briefly, something that you wrote in an earlier post, because when I first responded to it (last night), I was not "on my game":

It's obvious that any of the pirates could do better if they colluded

In fact, this is not obvious. Pirate A could not do better by colluding. Pirate A can obtain 98 coins by not colluding. S/he could not possibly do better than that by colluding.

Thanks for the additional links, Linda, but, unfortunately, I think that your attempts to marry this scenario with game theory are misplaced. The logic seems to me to be inexorable given the stated conditions, and nothing you have said has convinced me otherwise. It was fun considering that it might have been otherwise though, so I appreciate your raising this possibility.

As far as I know (like I said in my initial post), this isn’t supposed to be married with game theory given that I haven’t seen it discussed in that way (not that I had done any extensive reading on it). It’s just something which occurred to me to consider. I’m aware that I look at things differently from other people. Sometimes I’m curious about that.

And actually, on further reading from earlier today, I see that I wasn’t off-base when I considered it as I see that it is an extension of the Ultimatum game which is something which has been studied using game theory. Anything which you might say about the Pirate puzzle (with respect to the certainty of only one conclusion) applies even more strongly to the Ultimatum game. Yet we see from my earlier link that the conclusion is far from straightforward even for that much simpler game.

I want to address, briefly, something that you wrote in an earlier post, because when I first responded to it (last night), I was not "on my game":

In fact, this is not obvious. Pirate A could not do better by colluding. Pirate A can obtain 98 coins by not colluding. S/he could not possibly do better than that by colluding.

I agree. I don’t always bother to mention trivial exceptions. You’re supposed to be able to figure it out on your own.

Linda

[Laird]

it is an extension of the Ultimatum game

Nah. I strongly disagree. And nothing that you have presented has justified this assertion of yours which I've quoted. The logic of my solution to the puzzle (and, apparently, of your solution too, at least initially, based on what you've written), is, as far as I can see, sound. Game Theory is irrelevant to this puzzle.

From Wikipedia article on the Pirate game:

“It is a multi-player version of the ultimatum game.”

Linda

[Laird]

I stand corrected.

What I was trying to get at is that I don't think that applying game theory - as to the ultimatum game - leads to any different answer than the standard one for the pirate game.

Brexit sounds quite a lot like the Ultimate Game. Except Brexit never ends.

[Laird]

Which answer in this list is the correct answer to this question?

1. All of the below.
   
2. None of the below.
   
3. All of the above.
   
4. One of the above.
   
5. None of the above.
   
6. None of the above.