<p>The initial definition of a correlated equilibrium in [Aumann, Robert J. &quot;<a href="http://www.ma.huji.ac.il/raumann/pdf/Subjectivity%20and%20Correlation.pdf" rel="nofollow noreferrer">Subjectivity and correlation in randomized strategies.</a>&quot; <em>Journal of Mathematical Economics</em> 1.1 (1974): 67-96.] was with respect to some underlying probability space (more actually, to take account of the &quot;subjectivity part&quot;), and private information represented by <span class="math-container">$\sigma$</span>-algebras. The complicated measure theoretic probability machine was dispensed with in [Aumann, Robert J. &quot;<a href="http://www.ma.huji.ac.il/raumann/pdf/Correlated%20Equilibrium%20as%20an%20Expression.pdf" rel="nofollow noreferrer">Correlated equilibrium as an expression of Bayesian rationality.</a>&quot; <em>Econometrica: Journal of the Econometric Society</em> (1987): 1-18.] where a correlated equilibrium was defined, essentially, as a certain distribution over action profiles.</p>
<p>For great textbook treatments you can look at the books, both titled &quot;Game Theory&quot; by Roger Myerson (chapter 6 there), and by Eilon Solan, Michael Maschler, and Shmuel Zamir (chapter 8 there).</p>

CC BY-SA 4.0
2021-09-30T11:07:21.243Z
Since a correlated equilibrium is an expresson of Bayesian rationality, it means that there is some kind of connection between the Bayesian Nash Equilibrium and the Bayesian Correlated equilibrium? How is that so? I mean in the former the players act as if they decide to play therir strategy indepedently of the others while in the latter they correlate their strategies....is there some relation between the set of solutions in the BNE with the BCE?
Hunger Learn
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2021-09-30T11:07:58.587Z
maybe I should make a new question...if someone is going to answer the question above... :P
Hunger Learn
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2021-09-30T11:45:52.497Z
There is no direct connection to games of incomplete information.
Michael Greinecker
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2021-09-29T20:35:37.143Z
2021-09-29T20:35:37.143Z
Michael Greinecker
<p>Where can I find the definition of correlated equilibrium apart from <a href="https://en.wikipedia.org/wiki/Correlated_equilibrium" rel="nofollow noreferrer">here</a> and <a href="https://www.sciencedirect.com/science/article/abs/pii/0304406874900378" rel="nofollow noreferrer">the seminal paper of Aumman</a> ?</p>

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2021-09-28T14:47:32.397Z
[Osborne and Rubinstein](https://arielrubinstein.tau.ac.il/books/GT.pdf#page=60) have a brief treatment of correlated equilibrium. There's also Fudenberg and Tirole (Chap 2), which I believe you have access to.
Herr K.
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2021-09-29T14:21:27.847Z
@MichaelGreinecker Please post answers as answers.
Giskard
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2021-09-29T14:21:29.710Z
@HerrK. Please post answers as answers.
Giskard
<microeconomics><game-theory><nash-equilibrium>
Correlated equilibrium definition
Hunger Learn
# Correlated equilibrium definition

(Asked by: username_0 on 2021-09-28)

Where can I find the definition of correlated equilibrium apart from [here](https://en.wikipedia.org/wiki/Correlated_equilibrium) and [the seminal paper of Aumman](https://www.sciencedirect.com/science/article/abs/pii/0304406874900378) ?

**Tags:** microeconomics, game-theory, nash-equilibrium
> **Comments:**
> **username_1**: [Osborne and Rubinstein](https://arielrubinstein.tau.ac.il/books/GT.pdf#page=60) have a brief treatment of correlated equilibrium. There's also Fudenberg and Tirole (Chap 2), which I believe you have access to.  
> **username_2**: @MichaelGreinecker Please post answers as answers.  
> **username_2**: @HerrK. Please post answers as answers.  

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## 1 answers

### Answer by username_3 on 2021-09-29. Score: 3 | Accepted answer

The initial definition of a correlated equilibrium in [Aumann, Robert J. "[Subjectivity and correlation in randomized strategies.](http://www.ma.huji.ac.il/raumann/pdf/Subjectivity%20and%20Correlation.pdf)" *Journal of Mathematical Economics* 1.1 (1974): 67-96.] was with respect to some underlying probability space (more actually, to take account of the "subjectivity part"), and private information represented by $\sigma$-algebras. The complicated measure theoretic probability machine was dispensed with in [Aumann, Robert J. "[Correlated equilibrium as an expression of Bayesian rationality.](http://www.ma.huji.ac.il/raumann/pdf/Correlated%20Equilibrium%20as%20an%20Expression.pdf)" *Econometrica: Journal of the Econometric Society* (1987): 1-18.] where a correlated equilibrium was defined, essentially, as a certain distribution over action profiles.

For great textbook treatments you can look at the books, both titled "Game Theory" by Roger Myerson (chapter 6 there), and by Eilon Solan, Michael Maschler, and Shmuel Zamir (chapter 8 there).

> **Comments:**
> **username_0**: Since a correlated equilibrium is an expresson of Bayesian rationality, it means that there is some kind of connection between the Bayesian Nash Equilibrium and the Bayesian Correlated equilibrium? How is that so? I mean in the former the players act as if they decide to play therir strategy indepedently of the others while in the latter they correlate their strategies....is there some relation between the set of solutions in the BNE with the BCE?  
> **username_0**: maybe I should make a new question...if someone is going to answer the question above... :P  
> **username_3**: There is no direct connection to games of incomplete information.  

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