<p>No. In static games, common knowledge of rationality is equivalent to rationalizability. Bernheim, in "<a href="http://www.econ.yale.edu/~dirkb/teach/pdf/b/bernheim/1984%20rationalizable%20strategic%20behavior.pdf" rel="nofollow">Rationalizable Strategic Behavior</a>" (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.</p>

CC BY-SA 3.0
2015-04-06T18:41:11.007Z
You are looking at David Pearce's paper, but you should look at Doug Bernheim's paper in the same issue of Econometrica.
Tilman Borgers
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2015-04-06T18:45:35.517Z
My bad. Sorry : )
Metta World Peace
CC BY-SA 3.0
2015-04-06T17:09:55.957Z
2015-04-06T22:53:26.847Z
2015-04-06T22:53:26.847Z
Tilman Borgers
<p>In a highly controversial paper by Robert Aumann(see <a href="http://www.ma.huji.ac.il/raumann/pdf/36.pdf" rel="nofollow">here</a>), it is stated as a theorem:</p>

<blockquote>
  <p>In PI games, common knowledge of rationality implies backward induction.</p>
</blockquote>

<p>If we stick to the strong and controversial definition of rationality in the paper</p>

<blockquote>
  <p>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. </p>
</blockquote>

<p>Can we have some other implication, like, If a game admits a unique Nash equilibirum, does common knowledge of rationality implies Nash equilibirum?</p>

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2015-04-04T21:46:46.987Z
The first quote should be "In perfect information games, common ...", which makes it much less controversial.
The Almighty Bob
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2015-04-04T21:55:47.487Z
@TheAlmightyBob You're right! The controversies are different in two settings.
Metta World Peace
<game-theory><reference-request><nash-equilibrium>
If a game admits a unique Nash equilibirum, does common knowledge of rationality implies Nash equilibirum?
Metta World Peace
# If a game admits a unique Nash equilibirum, does common knowledge of rationality implies Nash equilibirum?

(Asked by: username_0 on 2015-04-04)

In a highly controversial paper by Robert Aumann(see [here](http://www.ma.huji.ac.il/raumann/pdf/36.pdf)), 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?

**Tags:** game-theory, reference-request, nash-equilibrium
> **Comments:**
> **username_1**: The first quote should be "In perfect information games, common ...", which makes it much less controversial.  
> **username_0**: @TheAlmightyBob You're right! The controversies are different in two settings.  

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## 1 answers

### Answer by username_2 on 2015-04-06. Score: 5 | Accepted answer

No. In static games, common knowledge of rationality is equivalent to rationalizability. Bernheim, in "[Rationalizable Strategic Behavior](http://www.econ.yale.edu/~dirkb/teach/pdf/b/bernheim/1984%20rationalizable%20strategic%20behavior.pdf)" (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.

> **Comments:**
> **username_2**: You are looking at David Pearce's paper, but you should look at Doug Bernheim's paper in the same issue of Econometrica.  
> **username_0**: My bad. Sorry : )  

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