If a game admits a unique Nash equilibirum, does common knowledge of rationality implies Nash equilibirum?
No. In static games, common knowledge of rationality is equivalent to rationalizability. Bernheim, in "Rationalizable Strategic Behavior" (Econometrica, July 1984) gives an example on page 1012 in Figure 1 of a normalform game in which there is a unique Nash equilibrium, yet multiple strategies are rationalizable.