2 . Interpreting Aumann’s theorem to mean what Aumann said it means… That is a fine semantic error buried deep within the English interpretation, but it makes the entire theorem worthless.
That was way too densely packed for my sleep-deprived brain to parse. Would you be willing to write a post (possibly Discussion post) spelling this out less succinctly? It seems important to get this idea out into the LW-sphere given how much cred the agreement theorem has around here.
It’s not just densely packed—it makes no sense unless you read the paper first, and read some other things necessary to understand that paper. I’d like to write a post—but not right now.
I know enough game theory to prove versions of Aumann’s theorem, but I have not read the paper, and your point in (2) makes no sense, period.
The correct game-theoretic statement of 1 knows that 2 knows that E is that E includes P1(P2(w)).
The meet of X and Y is about common knowledge. Saying that E is common knowledge is stronger than saying that 1 knows that 2 knows it. It also implies, for instance, that 2 knows that 1 knows that 2 knows it.
That was way too densely packed for my sleep-deprived brain to parse. Would you be willing to write a post (possibly Discussion post) spelling this out less succinctly? It seems important to get this idea out into the LW-sphere given how much cred the agreement theorem has around here.
It’s not just densely packed—it makes no sense unless you read the paper first, and read some other things necessary to understand that paper. I’d like to write a post—but not right now.
I know enough game theory to prove versions of Aumann’s theorem, but I have not read the paper, and your point in (2) makes no sense, period.
The correct game-theoretic statement of 1 knows that 2 knows that E is that E includes P1(P2(w)).
The meet of X and Y is about common knowledge. Saying that E is common knowledge is stronger than saying that 1 knows that 2 knows it. It also implies, for instance, that 2 knows that 1 knows that 2 knows it.