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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?${{}}$

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    $\begingroup$ One way to go through CS 1982 is to reproduce the proofs with simple examples. e.g. $\theta\sim U[0,1]$, $u^S=-(\theta-y-b)^2$, and $u^B=-(\theta-y)^2$. $\endgroup$
    – user28372
    Aug 18, 2020 at 16:49

1 Answer 1

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

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