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

耶鲁公开课 - 博弈论课程节选

Well I'll reveal the facts now: that in fact Ale knows that Kaj has a pink hat on his head.

我已经告诉你们了,艾尔只知道卡佳戴着粉色帽子

耶鲁公开课 - 博弈论课程节选

So Ale does not know that Kaj knows that there's a pink hat in the room.

所以艾尔不知道卡佳知道,这里有一定粉色的帽子

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

They can have a pink hat at the end of the class?

粉色的帽子就送给你了

耶鲁公开课 - 博弈论课程节选

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

耶鲁公开课 - 博弈论课程节选

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

But Ale does not know that Kaj knows that he is wearing a blue, a pink hat, and Kaj does not know that Ale knows that Kaj is wearing a pink hat.

但艾尔不知道卡佳知道他戴着粉色帽子,卡佳也不知道艾尔知道,卡佳戴着粉色帽子

耶鲁公开课 - 博弈论课程节选