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gjm comments on [LINK] Scott Aaronson: Common knowledge and Aumann's agreement theorem - Less Wrong Discussion

13 Post author: gjm 17 August 2015 08:41AM

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Comment author: gjm 04 December 2015 02:46:23PM 1 point [-]

Common knowledge means I know, and I know that you know, and I know that you know that he knows, and she knows that I know that you know that he knows, and so on -- any number of iterations.

Each child sees 99 muddy foreheads and therefore knows n >= 99. Each child can tell that each other child knows n >= 98. But, e.g., it isn't true that A knows B knows C knows that n >= 98; only that A knows B knows C knows that n>=97: each link in the chain reduces the number by 1. So for no k>0 is it common knowledge that n>=k.

Comment author: GMHowe 22 December 2015 12:20:23AM 0 points [-]

Thanks, I did end up figuring out my error.