<p><span class="math-container">$U^S(\bar y,\bar m,b)=\max_{y\in Y}U^S(y,\bar m,b)$</span> is standard notation that says <span class="math-container">$\bar y$</span> is the action (taken by receiver) that would maximize sender's utility given message <span class="math-container">$\bar m$</span> and bias parameter <span class="math-container">$b$</span>. In other words, sender would prefer receiver to choose <span class="math-container">$\bar y$</span> when he sends message <span class="math-container">$\bar m$</span>. Sender's maximized utility is <span class="math-container">$U^S(\bar y,\bar m,b)$</span>.</p>
<p>For a simpler introduction to Crawford and Sobel, you can read Chapter 18 of <a href="https://books.google.ca/books/about/Game_Theory.html?id=_4OqAaITAWMC&amp;printsec=frontcover#v=onepage&amp;q&amp;f=false" rel="noreferrer">Tadelis's Game Theory textbook</a> on cheap talk games.</p>

CC BY-SA 4.0
2020-08-18T15:19:31.203Z
2020-08-18T15:19:31.203Z
Herr K.
<p>I am a master student, currently reading this paper for fun during the break. I got lost during the part <span class="math-container">$U^S(\bar y, \bar m, b) = \max_{y \in Y} U^S(y,\bar m, b)$</span> on page 5. I dont understand why they wrote this without any explanation. Then I got lost again during proof of lemma 1. Should I read other paper first before approaching this?<span class="math-container">${{}}$</span></p>

<game-theory><bayesian-game>
I cannot understand Sobel & Crawford 1982 (cheap talk)
Aspiring Economist
# I cannot understand Sobel & Crawford 1982 (cheap talk)

(Asked by: username_0 on 2020-08-18)

I am a master student, currently reading this paper for fun during the break. I got lost during the part $U^S(\bar y, \bar m, b) = \max\_{y \in Y} U^S(y,\bar m, b)$ on page 5. I dont understand why they wrote this without any explanation. Then I got lost again during proof of lemma 1. Should I read other paper first before approaching this?${{}}$

**Tags:** game-theory, bayesian-game


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## 1 answers

### Answer by username_1 on 2020-08-18. Score: 5

$U^S(\bar y,\bar m,b)=\max\_{y\in Y}U^S(y,\bar m,b)$ is standard notation that says $\bar y$ is the action (taken by receiver) that would maximize sender's utility given message $\bar m$ and bias parameter $b$. In other words, sender would prefer receiver to choose $\bar y$ when he sends message $\bar m$. Sender's maximized utility is $U^S(\bar y,\bar m,b)$.

For a simpler introduction to Crawford and Sobel, you can read Chapter 18 of [Tadelis's Game Theory textbook](https://books.google.ca/books/about/Game_Theory.html?id=_4OqAaITAWMC&printsec=frontcover#v=onepage&q&f=false) on cheap talk games.


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