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 violate common knowledge of rationality. Is there a contradiction here? This entry will not survey the extensive literature on this question. The reader can consult the references in Bruin 2010. Our point here is rather that how one looks at this potential paradox hinges on the way the players will revise their beliefs in “future” rationality in the light of observing a move that would be “irrational” under common knowledge of rationality.