So it's true that Ale knows that at least one person in the room has a pink hat on their head.

所以艾尔确实知道,至少有一个人戴着粉色的帽子

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And it's true that Kaj knows that Ale has a pink hat on his head.

而且卡佳也知道艾尔戴着粉色的帽子

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So again, they both know that someone in the room has a pink hat on their head: it is mutual knowledge that there's a pink hat in the room.

但是他们都知道,至少有一个人戴着粉色帽子,至少有一顶粉色帽子是相互知识

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Here is a fact, so is it common knowledge that -- is it common knowledge that at least one of these people has a pink hat on their head?

我这样说这是共同知识吗,至少有一个人戴着粉色的帽子,这是共同知识吗

耶鲁公开课 - 博弈论课程节选