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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?

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  • $\begingroup$ The first quote should be "In perfect information games, common ...", which makes it much less controversial. $\endgroup$ – The Almighty Bob Apr 4 '15 at 21:46
  • $\begingroup$ @TheAlmightyBob You're right! The controversies are different in two settings. $\endgroup$ – Metta World Peace Apr 4 '15 at 21:55
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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.

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  • $\begingroup$ You are looking at David Pearce's paper, but you should look at Doug Bernheim's paper in the same issue of Econometrica. $\endgroup$ – TMB Apr 6 '15 at 18:41
  • $\begingroup$ My bad. Sorry : ) $\endgroup$ – Metta World Peace Apr 6 '15 at 18:45

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