Friday, August 1, 2008

Common Knowledge

I was just reading a paper called "The Argentina Crisis: Bad Luck, Bad Management, Bad Politics, Bad Advice" and came across the following:

At a time when the IMF had given no real indications that further funds would be forthcoming, there was now an admission that there was no prospect of any private sector funding either. In the terminology of game theory, this might be thought of as an event that changed the degree of ‘common knowledge’ among investors.
Common knowledge in game theory sounded interesting so I looked it up in Wikipedia. Here's a little puzzle that provides a taste of the concept.
It is common to introduce the idea of common knowledge by some variant of the following logic puzzle:[2] On an island, there are k people who have blue eyes, and the rest of the people have green eyes. There is at least one blue-eyed person on the island (k >= 1). If a person ever knows herself to have blue eyes, she must leave the island at dawn the next day. Each person can see every other person's eye color, there are no mirrors, and there is no discussion of eye color. At some point, an outsider comes to the island and makes the following public announcement, heard and understood by all people on the island: "at least one of you has blue eyes". The problem: Assuming all persons on the island are truthful and completely logical, what is the eventual outcome?

The answer is that, on the k dawns after the announcement, all the blue-eyed people will leave the island.

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