Yes, what's happening in the Monty Hall problem is not common knowledge, but it is knowledge about knowledge. To use a fancy term, recursive mentalizing, where mentalizing means getting into someone else's head, trying to figure out what they know. Recursive mentalizing is trying to get inside their head, and when they're trying to get inside your head, as you're trying to get inside their head at an item. So that's common knowledge. In the case of the Monty Hall problem, it's private knowledge,
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