Comments on: The bottle imp paradox http://mindyourdecisions.com/blog/2010/01/05/the-bottle-imp-paradox/ Articles on game theory and personal finance Thu, 29 Jul 2010 12:43:59 -0500 hourly 1 http://wordpress.org/?v=3.0 By: Mauricio http://mindyourdecisions.com/blog/2010/01/05/the-bottle-imp-paradox/comment-page-1/#comment-6279 Mauricio Thu, 28 Jan 2010 00:55:36 +0000 http://mindyourdecisions.com/blog/?p=1866#comment-6279 There's one key difference between the greater fool theory and the bottle imp paradox. The prices in the bottle imp paradox goes down and have a clear lower limit, zero. The prices in the greater fool theory goes up and have no theoretical upper limit. Actually, prices CAN keep going up indefinitely and it is called inflation. If stock prices goes up faster or slower than average inflation is another story. There’s one key difference between the greater fool theory and the bottle imp paradox.

The prices in the bottle imp paradox goes down and have a clear lower limit, zero. The prices in the greater fool theory goes up and have no theoretical upper limit.

Actually, prices CAN keep going up indefinitely and it is called inflation. If stock prices goes up faster or slower than average inflation is another story.

]]> By: Gamer http://mindyourdecisions.com/blog/2010/01/05/the-bottle-imp-paradox/comment-page-1/#comment-6194 Gamer Wed, 06 Jan 2010 21:08:15 +0000 http://mindyourdecisions.com/blog/?p=1866#comment-6194 The Greater Fool Theory relies on the fact that you don't know everyone in the world. If this was a game (not the card game) but a game that plays out just like the story, the difference is it's a hand full of people that could buy the bottle (maybe 20) and you knew everyone, would people still play or will they think more rationally? Of course in the story you don't even have to wait for the madness of others; simply wish that a currency was lower (or the currency you paid for was higher). Though, I bet that would create madness. The Greater Fool Theory relies on the fact that you don’t know everyone in the world. If this was a game (not the card game) but a game that plays out just like the story, the difference is it’s a hand full of people that could buy the bottle (maybe 20) and you knew everyone, would people still play or will they think more rationally?

Of course in the story you don’t even have to wait for the madness of others; simply wish that a currency was lower (or the currency you paid for was higher). Though, I bet that would create madness.

]]> By: michael webster http://mindyourdecisions.com/blog/2010/01/05/the-bottle-imp-paradox/comment-page-1/#comment-6191 michael webster Wed, 06 Jan 2010 15:05:14 +0000 http://mindyourdecisions.com/blog/?p=1866#comment-6191 The bottle imp problem is a version of what philosophers call a sorites inference. Here is a nice review of the problems a sorites form can generate: http://artsci.wustl.edu/~philos/people/sorensen/PAPERS/Precis%20of%20Vagueness%20and%20C.pdf The bottle imp problem is a version of what philosophers call a sorites inference. Here is a nice review of the problems a sorites form can generate:
http://artsci.wustl.edu/~philos/people/sorensen/PAPERS/Precis%20of%20Vagueness%20and%20C.pdf

]]> By: michael webster http://mindyourdecisions.com/blog/2010/01/05/the-bottle-imp-paradox/comment-page-1/#comment-6188 michael webster Wed, 06 Jan 2010 14:34:50 +0000 http://mindyourdecisions.com/blog/?p=1866#comment-6188 Presh, I like this story and was not familiar with it. The conditions of the game rule out J's ingenious solution because you cannot give the bottle away, which I assume also covers paying someone to take the bottle. I also like Scott's solution, which could be generalized to having the genie find a person damned already but who wants to end his/her own life in wealth. There is another obvious solution: make the payments in real and not nominal dollars. A penny today is worth more than a penny tomorrow, so the bottle can be resold. What is interesting, to me, is that this problem may prove to be an antidote to network marketers who are constantly wrong about the span of their network of friends and believe that it is possible to sell an opportunity to sell an opportunity to sell x, when the opportunity to sell x is a lousy deal. A striking example of the greater fool theory. Presh, I like this story and was not familiar with it.
The conditions of the game rule out J’s ingenious solution because you cannot give the bottle away, which I assume also covers paying someone to take the bottle.

I also like Scott’s solution, which could be generalized to having the genie find a person damned already but who wants to end his/her own life in wealth.

There is another obvious solution: make the payments in real and not nominal dollars. A penny today is worth more than a penny tomorrow, so the bottle can be resold.

What is interesting, to me, is that this problem may prove to be an antidote to network marketers who are constantly wrong about the span of their network of friends and believe that it is possible to sell an opportunity to sell an opportunity to sell x, when the
opportunity to sell x is a lousy deal. A striking example of the greater fool theory.

]]> By: Eyal http://mindyourdecisions.com/blog/2010/01/05/the-bottle-imp-paradox/comment-page-1/#comment-6185 Eyal Wed, 06 Jan 2010 08:22:24 +0000 http://mindyourdecisions.com/blog/?p=1866#comment-6185 One more thing, @Scott: The pop quiz paradox is easy to solve. The confusion is about surprise and predictability. When you flip a coin, you can't predict how it will land but neither heads or tails would be a surprise. (If it turned into a banana, that would be a surprise.) Same for the pop quiz. You can't predict when it'll happen but when it does, it won't be a surprise. One more thing, @Scott: The pop quiz paradox is easy to solve. The confusion is about surprise and predictability. When you flip a coin, you can’t predict how it will land but neither heads or tails would be a surprise. (If it turned into a banana, that would be a surprise.)

Same for the pop quiz. You can’t predict when it’ll happen but when it does, it won’t be a surprise.

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