If the game reaches node v2, common knowledge of rationality has already been violated by player A's prior move.

This result has been extensively discussed. The standard ground of contention is that common knowledge of rationality used in this argument seems self-defeating, at least intuitively. Recall that we asked what would \(B\) do at node \(v_2\) under common knowledge of rationality, and we concluded that he would choose \(O_2\). But, if the game ever reaches that state, then, by the theorem above, \(B\) has to conclude that either \(A\) is not rational, or that she does not know that he is. Both vio