# I cannot understand Sobel & Crawford 1982 (cheap talk)

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?$${{}}$$

• 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 $u^B=-(\theta-y)^2$.
– user28372
Aug 18, 2020 at 16:49

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