Comments on: The necktie paradox http://mindyourdecisions.com/blog/2009/12/15/the-necktie-paradox/ Articles on game theory and personal finance Tue, 22 May 2012 15:59:00 +0000 hourly 1 http://wordpress.org/?v=3.3.2 By: Benjamin Vitale http://mindyourdecisions.com/blog/2009/12/15/the-necktie-paradox/comment-page-1/#comment-6032 Benjamin Vitale Thu, 17 Dec 2009 00:18:22 +0000 http://mindyourdecisions.com/blog/?p=1830#comment-6032 Presh, Cecil, You're right, I was wrong. Presh, Cecil,
You’re right, I was wrong.

]]> By: Presh Talwalkar http://mindyourdecisions.com/blog/2009/12/15/the-necktie-paradox/comment-page-1/#comment-6013 Presh Talwalkar Tue, 15 Dec 2009 18:29:16 +0000 http://mindyourdecisions.com/blog/?p=1830#comment-6013 <b><em>gmsc</b></em>: Thanks for the links. I will look into the two envelopes math and I hope to do a writeup of this. <b><em>Benjamin</b></em>: Actually what you wrote is the incorrect reasoning. You either end up with both ties or with no ties. If y > z, the expression is either: 0.5(z) - 0.5(z) = 0 [payoffs in terms of "profit"] Or 0.5(y+z) - 0.5(y+z) = 0 [payoffs in terms of "revenue"] The second expression being what Cecil wrote. gmsc: Thanks for the links. I will look into the two envelopes math and I hope to do a writeup of this.

Benjamin: Actually what you wrote is the incorrect reasoning. You either end up with both ties or with no ties. If y > z, the expression is either:

0.5(z) – 0.5(z) = 0 [payoffs in terms of "profit"]

Or

0.5(y+z) – 0.5(y+z) = 0 [payoffs in terms of "revenue"]

The second expression being what Cecil wrote.

]]> By: WOPR http://mindyourdecisions.com/blog/2009/12/15/the-necktie-paradox/comment-page-1/#comment-6012 WOPR Tue, 15 Dec 2009 18:14:23 +0000 http://mindyourdecisions.com/blog/?p=1830#comment-6012 "The only winning move is not to play" “The only winning move is not to play”

]]> By: Cecil http://mindyourdecisions.com/blog/2009/12/15/the-necktie-paradox/comment-page-1/#comment-6008 Cecil Tue, 15 Dec 2009 14:32:44 +0000 http://mindyourdecisions.com/blog/?p=1830#comment-6008 Benjamin, that doesn't make sense. Both parties in a simple wager can't have an expected gain. The key is that when you lose the bet, you lose the more expensive tie - so the expected value in winnings is (0.5)(y+z) - (0.50)(y+z) = 0. Benjamin, that doesn’t make sense. Both parties in a simple wager can’t have an expected gain.

The key is that when you lose the bet, you lose the more expensive tie – so the expected value in winnings is

(0.5)(y+z) – (0.50)(y+z) = 0.

]]> By: Benjamin Vitale http://mindyourdecisions.com/blog/2009/12/15/the-necktie-paradox/comment-page-1/#comment-6004 Benjamin Vitale Tue, 15 Dec 2009 10:17:11 +0000 http://mindyourdecisions.com/blog/?p=1830#comment-6004 Presh, Say, the less expensive necktie has value "y", and the more expensive one has the value y+z with z > 0. Assuming that both men have an equal chance of being correct, the expected value in winnings for either man is, (0.50)(y + z) - (0.50)(y) = (0.50)z Both men are expected to make money if they bet. So both men are correct in choosing to bet. Presh,

Say, the less expensive necktie has value “y”, and
the more expensive one has the value y+z with z > 0.

Assuming that both men have an equal chance of being correct, the expected value in winnings for either man is,

(0.50)(y + z) – (0.50)(y) = (0.50)z

Both men are expected to make money if they bet.
So both men are correct in choosing to bet.

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