<p>Would be strange to write it that way.</p>
<p>If you had to define something like that, just do the following:</p>
<p>Start with a type space <span class="math-container">$(T,\mu)$</span> with probability measure <span class="math-container">$\mu$</span>.</p>
<p>Let <span class="math-container">$\sigma: T \rightarrow \Delta(A)$</span>.</p>
<p>Then <span class="math-container">$\mathbb{P}(a) =\mu(\sigma^{-1}(a))$</span>.</p>

CC BY-SA 4.0
2022-01-20T16:17:20.670Z
you are right. This is the way... Thanks
Hunger Learn
CC BY-SA 4.0
2022-01-19T19:32:36.020Z
2022-01-19T19:32:36.020Z
Walrasian Auctioneer
<p>I have a simple question though confusio for me. In game theory we usully write thet a strategy is a mapping from the set of types <span class="math-container">$T$</span> to the simplex set of actions (refering to mixed mixed strategies) and we write</p>
<p><span class="math-container">$$\sigma:T\to\Delta(A)$$</span></p>
<p>Is it right to write the following
<span class="math-container">$$\sigma(t)=\mathbb{P}r\times a$$</span>
where <span class="math-container">$\mathbb{P}r$</span> is the probability that the profile of strategies <span class="math-container">$a$</span> is played?</p>

CC BY-SA 4.0
2022-01-19T16:06:54.313Z
Have you seen this $\mathbb{P}r\times$ notation anywhere, or did you come up with it?
Giskard
CC BY-SA 4.0
2022-01-19T21:28:58.290Z
I have never seen notation like that and would be confused by it.
Michael Greinecker
<mathematical-economics><game-theory><bayesian-game>
Is the following claim written with the right way?
Hunger Learn
# Is the following claim written with the right way?

(Asked by: username_0 on 2022-01-19)

I have a simple question though confusio for me. In game theory we usully write thet a strategy is a mapping from the set of types $T$ to the simplex set of actions (refering to mixed mixed strategies) and we write

$$\sigma:T\to\Delta(A)$$

Is it right to write the following
$$\sigma(t)=\mathbb{P}r\times a$$
where $\mathbb{P}r$ is the probability that the profile of strategies $a$ is played?

**Tags:** mathematical-economics, game-theory, bayesian-game
> **Comments:**
> **username_1**: Have you seen this $\mathbb{P}r\times$ notation anywhere, or did you come up with it?  
> **username_2**: I have never seen notation like that and would be confused by it.  

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## 1 answers

### Answer by username_3 on 2022-01-19. Score: 5 | Accepted answer

Would be strange to write it that way.

If you had to define something like that, just do the following:

Start with a type space $(T,\mu)$ with probability measure $\mu$.

Let $\sigma: T \rightarrow \Delta(A)$.

Then $\mathbb{P}(a) =\mu(\sigma^{-1}(a))$.

> **Comments:**
> **username_0**: you are right. This is the way... Thanks  

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