In a highly controversial paper by Robert Aumann(see here), it is stated as a theorem:
In PI games, common knowledge of rationality implies backward induction.
If we stick to the strong and controversial definition of rationality in the paper
Rationality of a player means that he is a habitual payoff maximizer: that no matter where he finds himself, at which vertex,he will not knowingly continue with a strategy that yields him less than he could have gotten with a different strategy.
Can we have some other implication, like, If a game admits a unique Nash equilibirum, does common knowledge of rationality implies Nash equilibirum?