Yet another game theory puzzle, one that is always fun to come across, especially on Terence Tao’s blog. In the version I know the islanders are less devoted to their religion and more jealous of their wives, but the point is the same. Does it make any difference when a fact that everybody already knows is publicly announced ?
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3 comments
April 17, 2011 at 8:40 am
Joseph
I dont see how and I’ve yet to see a comment, and i have read HUNDREDS of them on both Terry’s blog and on XKCD and in forums, that explains it in a way that doesn’t seem very hand-wavy to me, I have also read the Wikepedia article and it gives no sources, except on “structurally equivalent” version from some behavioural economists 2000 paper, are you aware of any text, monograph, textbook or other source where any attempt is made to explain this puzzle in a comprehensive way that makes allowances for a skeptical student?… I am beginning to think the whole thing is a hoax.
April 18, 2011 at 2:47 am
chris
Joseph, just start out from n=1: What would happen if there was but 1 blue-eyed native on the island? What would happen if there were two? …
April 18, 2011 at 11:35 pm
Eran
I actually don’t know of any game theory text that analyzes this puzzle formally, which is a bit strange since this is the most beatiful demonstration I know for common knowledge. I think the reason is that game theorists are used to represent knowledge as a partition of a state space, and in this puzzle, the state space will be too large to work with.