<blockquote>
<p>Can there be a PBE in which both types do not get any education (i.e. <span class="math-container">$e=0$</span> for both)?</p>
</blockquote>
<p>Yes, workers' strategies <span class="math-container">$e^*(\theta_L)=e^*(\theta_H)=0$</span> and a wage function <span class="math-container">$w^*(e)$</span> satisfying: (i) <span class="math-container">$w^*(0)=E[\theta]$</span> and (ii) for all <span class="math-container">$e\ge0$</span>, <span class="math-container">$w^*(e)$</span> is no higher than <span class="math-container">$u_H^0$</span> --- the high-type's indifference curve crossing point <span class="math-container">$(0,E[\theta])$</span> --- form such a PBE. For example, one possible such PBE is graphically depicted as follows:</p>
<p><a href="https://i.sstatic.net/ZKYv7.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZKYv7.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-09-07T17:47:21.340Z
Thank you for your answer, this is what I had in mind :)
Maybeline Lee
CC BY-SA 4.0
2021-09-07T17:33:10.850Z
2021-09-07T17:33:10.850Z
Herr K.
<p>Consider two firms are offering contracts to an employee who has either high or
low productivity (<span class="math-container">$θ_H$</span> or <span class="math-container">$θ_L$</span>, with <span class="math-container">$θ_H &gt; θ_L$</span>). The employee can acquire education <span class="math-container">$e$</span> which is costly but does not increase productivity; the cost of education is strictly
increasing and convex in e but strictly decreasing in <span class="math-container">$θ$</span>. The firms can observe <span class="math-container">$e$</span> but
not <span class="math-container">$θ$</span> before deciding which wage <span class="math-container">$w$</span> to offer the employee. If the employee does not
accept any contract, she gets wage <span class="math-container">$0$</span>. Can there be a PBE in which both types do not get any education (i.e. <span class="math-container">$e = 0$</span> for both)?</p>
<p>My understanding is that we are in pooling equilibrium and the outcome of this scenario where neither type gets an education is the same as if there was no signal. Can there be an equilibrium? There could be if <span class="math-container">$\theta_H$</span> doesn't deviate by changing the education level. If we had to draw the figure would it be something similar to this but with exceptions were <span class="math-container">$\theta_L=E[\theta]$</span> and just remove the wage schedule since the education level is <span class="math-container">$e_H=e_L=0$</span></p>
<p><a href="https://i.sstatic.net/OL2cc.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OL2cc.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-09-06T17:31:28.493Z
Looks like you already have the answer. Are you just seeking confirmation?
Herr K.
CC BY-SA 4.0
2021-09-06T19:22:59.227Z
Yes, I wasn't sure if my reasoning was correct as I'm not very familiar with these topics, so I just wanted to check if my answer is suitable or not
Maybeline Lee
<microeconomics><signaling>
Competitive equilibrium in signaling games
Maybeline Lee
# Competitive equilibrium in signaling games

(Asked by: username_0 on 2021-09-06)

Consider two firms are offering contracts to an employee who has either high or
low productivity ($θ\_H$ or $θ\_L$, with $θ\_H > θ\_L$). The employee can acquire education $e$ which is costly but does not increase productivity; the cost of education is strictly
increasing and convex in e but strictly decreasing in $θ$. The firms can observe $e$ but
not $θ$ before deciding which wage $w$ to offer the employee. If the employee does not
accept any contract, she gets wage $0$. Can there be a PBE in which both types do not get any education (i.e. $e = 0$ for both)?

My understanding is that we are in pooling equilibrium and the outcome of this scenario where neither type gets an education is the same as if there was no signal. Can there be an equilibrium? There could be if $\theta\_H$ doesn't deviate by changing the education level. If we had to draw the figure would it be something similar to this but with exceptions were $\theta\_L=E[\theta]$ and just remove the wage schedule since the education level is $e\_H=e\_L=0$

[![enter image description here](https://i.sstatic.net/OL2cc.png)](https://i.sstatic.net/OL2cc.png)

**Tags:** microeconomics, signaling
> **Comments:**
> **username_1**: Looks like you already have the answer. Are you just seeking confirmation?  
> **username_0**: Yes, I wasn't sure if my reasoning was correct as I'm not very familiar with these topics, so I just wanted to check if my answer is suitable or not  

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## 1 answers

### Answer by username_1 on 2021-09-07. Score: 1 | Accepted answer

> Can there be a PBE in which both types do not get any education (i.e. $e=0$ for both)?

Yes, workers' strategies $e^\*(\theta\_L)=e^\*(\theta\_H)=0$ and a wage function $w^\*(e)$ satisfying: (i) $w^\*(0)=E[\theta]$ and (ii) for all $e\ge0$, $w^\*(e)$ is no higher than $u\_H^0$ --- the high-type's indifference curve crossing point $(0,E[\theta])$ --- form such a PBE. For example, one possible such PBE is graphically depicted as follows:

[![enter image description here](https://i.sstatic.net/ZKYv7.png)](https://i.sstatic.net/ZKYv7.png)

> **Comments:**
> **username_0**: Thank you for your answer, this is what I had in mind :)  

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