I cannot understand Sobel & Crawford 1982 (cheap talk)

Question

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?${{}}$

Herr K. · Answer

$U^S(bar y,bar m,b)=max_{yin Y}U^S(y,bar m,b)$ 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 on cheap talk games.

I cannot understand Sobel & Crawford 1982 (cheap talk)

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