<p><span class="math-container">$BA'$</span> doesn't work because <span class="math-container">$A'$</span> is <em>not</em> a best response to <span class="math-container">$X$</span>, which is a best response to <span class="math-container">$B$</span>.</p>

CC BY-SA 4.0
2021-04-17T12:27:05.450Z
Can you please elaborate on why A' is not a best response to X? (P1 is getting a higher payoff that way).
rand1
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2021-04-17T12:46:40.153Z
@ryan1: P1 gets 4 from A' but gets 6 from playing B' when P2 plays X. So B' is a better response to X than A'
Herr K.
CC BY-SA 4.0
2021-04-17T01:28:26.263Z
2021-04-17T01:28:26.263Z
Herr K.
<blockquote>
<p>Exercise Question 2, Chapter 28, Strategy: An Introduction to Game Theory 3rd Edition by Joel Watson</p>
</blockquote>
<p><a href="https://i.sstatic.net/DTSVY.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DTSVY.jpg" alt="enter image description here" /></a></p>
<p>In part (a) of the question, we have to check if any separating perfect Bayesian equilibrium exists.</p>
<p>Now the solution manual says that there is not any separating perfect Bayesian equilibrium.</p>
<p>My attempt:</p>
<p>The separating strategy profiles are AB’ and BA’.</p>
<p>Let us take AB’. P1 plays B’, then P2 knows that P1 must be L-type. P2 will prefer playing Y, so P1 will not prefer playing B’. No PBE here.</p>
<p>Let us take BA’. P1 plays B then P2 knows that P1 is H-type. P2 prefers playing X, so P1 will not prefer deviating from B since 6 &gt; 4. So, A’B is a separating perfect Bayesian equilibrium here.</p>
<p>What is wrong with my understanding here?</p>

<game-theory><bayesian-game>
Find a separating perfect Bayesian equilibrium
rand1
# Find a separating perfect Bayesian equilibrium

(Asked by: username_0 on 2021-04-17)

> Exercise Question 2, Chapter 28, Strategy: An Introduction to Game Theory 3rd Edition by Joel Watson

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

In part (a) of the question, we have to check if any separating perfect Bayesian equilibrium exists.

Now the solution manual says that there is not any separating perfect Bayesian equilibrium.

My attempt:

The separating strategy profiles are AB’ and BA’.

Let us take AB’. P1 plays B’, then P2 knows that P1 must be L-type. P2 will prefer playing Y, so P1 will not prefer playing B’. No PBE here.

Let us take BA’. P1 plays B then P2 knows that P1 is H-type. P2 prefers playing X, so P1 will not prefer deviating from B since 6 > 4. So, A’B is a separating perfect Bayesian equilibrium here.

What is wrong with my understanding here?

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

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## 1 answers

### Answer by username_1 on 2021-04-17. Score: 3 | Accepted answer

$BA'$ doesn't work because $A'$ is *not* a best response to $X$, which is a best response to $B$.

> **Comments:**
> **username_0**: Can you please elaborate on why A' is not a best response to X? (P1 is getting a higher payoff that way).  
> **username_1**: @ryan1: P1 gets 4 from A' but gets 6 from playing B' when P2 plays X. So B' is a better response to X than A'  

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