Comments on: Game theory and the math of infinity http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/ Articles on game theory and personal finance Sun, 20 May 2012 23:31:00 +0000 hourly 1 http://wordpress.org/?v=3.3.2 By: Alexander http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-12640 Alexander Wed, 23 Nov 2011 05:48:20 +0000 http://mindyourdecisions.com/blog/?p=807#comment-12640 If you limit it to integers and have a initial group of 1 to 10, alice can use the same logic. Also if Alice chooses 0.001-0.999 and initially chooses 0.002 then all she needs to do is make sure x is less than 0.999 If Bob picks ANY number in sub set S (S1, S3, S9001...) Alice can't lose even if she tries to. So Bob's strategy doesn't work, no matter if it's part of a set with countable infinite number or not, the original set could be all numbers = to 1+1/n where n is a positive interger. If you limit it to integers and have a initial group of 1 to 10, alice can use the same logic.
Also if Alice chooses 0.001-0.999 and initially chooses 0.002 then all she needs to do is make sure x is less than 0.999 If Bob picks ANY number in sub set S (S1, S3, S9001…) Alice can’t lose even if she tries to. So Bob’s strategy doesn’t work, no matter if it’s part of a set with countable infinite number or not, the original set could be all numbers = to 1+1/n where n is a positive interger.

]]> By: Sauron http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-12087 Sauron Wed, 19 Oct 2011 01:16:36 +0000 http://mindyourdecisions.com/blog/?p=807#comment-12087 This seems to be just a game created out of Cantor's first uncountability proof. While useful for explaining the concept to game theorists, it's not particularly novel. This seems to be just a game created out of Cantor’s first uncountability proof. While useful for explaining the concept to game theorists, it’s not particularly novel.

]]> By: A math game of dodgeball - Mind Your Decisions http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-12077 A math game of dodgeball - Mind Your Decisions Tue, 18 Oct 2011 05:02:47 +0000 http://mindyourdecisions.com/blog/?p=807#comment-12077 [...] As you can see, game theory can make set theory a bit more interesting. If you like this post, you will also like a previous one I wrote about a game that proves the real numbers are uncountably large. [...] [...] As you can see, game theory can make set theory a bit more interesting. If you like this post, you will also like a previous one I wrote about a game that proves the real numbers are uncountably large. [...]

]]> By: Presh Talwalkar http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-6094 Presh Talwalkar Wed, 23 Dec 2009 19:04:43 +0000 http://mindyourdecisions.com/blog/?p=807#comment-6094 <b><em>Chris</b></em>: You're right! Bob can definitely throw the game, just as one could lose in tic-tac-toe or in <a href="http://en.wikipedia.org/wiki/Hex_(board_game)" rel="nofollow">Hex</a> (a game with an unknown but provably winnable strategy for the first player). So whether Bob does win a particular game is irrelevant to the proof. And in fact, this game is not really practical to play--who has potentially infinite time to play a game? Chris: You’re right! Bob can definitely throw the game, just as one could lose in tic-tac-toe or in Hex (a game with an unknown but provably winnable strategy for the first player).

So whether Bob does win a particular game is irrelevant to the proof. And in fact, this game is not really practical to play–who has potentially infinite time to play a game?

]]> By: Chris http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-6088 Chris Tue, 22 Dec 2009 20:24:56 +0000 http://mindyourdecisions.com/blog/?p=807#comment-6088 Just because Bob CAN win, doesn't mean he WILL necessarily win. How would Bob know which subset Alice picked before the game started? Just because Bob CAN win, doesn’t mean he WILL necessarily win. How would Bob know which subset Alice picked before the game started?

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