<p>Formally, a NE is indeed a different mathematical object than a CE. But, roughly speaking, the probability distribution on outcomes generated by a NE is a CE. This is what is really meant when saying that &quot;a NE is a special case of a CE.&quot;</p>

CC BY-SA 4.0
2022-12-29T11:26:14.577Z
2022-12-29T11:26:14.577Z
VARulle
<p>In a Mixed Strategy Nash Equilibrium, each player constructs their own probability distribution over the set of their respective possible strategies.</p>
<p>In a Correlated Equilibrium or a Coarse Correlated Equilibrium, there is only one global probability distribution which the players must take as given, and it is defined over a game's possible outcomes rather than each player's possible strategies.</p>
<p>These feel like fairly different animals.  Why are Mixed Strategy Nash Equilibria special cases of Correlated Equilibria and Coarse Correlated Equilibria?</p>

CC BY-SA 4.0
2022-12-29T12:28:33.260Z
What do you mean by “each player constructs their own probability distribution over the set of their respective possible strategies”? In NE every player knows strategies of all players, and it is out is scope who constructed the strategies.
LudwigNagasena
<game-theory><nash-equilibrium><probability><mechanism-design><solution-concept>
Why are Mixed Strategy Nash Equilibria special cases of Correlated Equilibria and Coarse Correlated Equilibria?
user10478
# Why are Mixed Strategy Nash Equilibria special cases of Correlated Equilibria and Coarse Correlated Equilibria?

(Asked by: username_0 on 2022-12-28)

In a Mixed Strategy Nash Equilibrium, each player constructs their own probability distribution over the set of their respective possible strategies.

In a Correlated Equilibrium or a Coarse Correlated Equilibrium, there is only one global probability distribution which the players must take as given, and it is defined over a game's possible outcomes rather than each player's possible strategies.

These feel like fairly different animals. Why are Mixed Strategy Nash Equilibria special cases of Correlated Equilibria and Coarse Correlated Equilibria?

**Tags:** game-theory, nash-equilibrium, probability, mechanism-design, solution-concept
> **Comments:**
> **username_1**: What do you mean by “each player constructs their own probability distribution over the set of their respective possible strategies”? In NE every player knows strategies of all players, and it is out is scope who constructed the strategies.  

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## 1 answers

### Answer by username_2 on 2022-12-29. Score: 4 | Accepted answer

Formally, a NE is indeed a different mathematical object than a CE. But, roughly speaking, the probability distribution on outcomes generated by a NE is a CE. This is what is really meant when saying that "a NE is a special case of a CE."


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