<p>The two (pure) Nash equilibrium in this game is (Betray, Silent) and (Silent, Betray).</p>
<p>Let us see why (Betray, Silent) is an equilibrium.</p>
<p><strong>Let us look at person A.</strong></p>
<p>Person B is playing Silent.</p>
<ol>
<li>If she plays Betray, she gets <span class="math-container">$2$</span>.</li>
<li>If she deviates to Silent, she gets <span class="math-container">$1$</span>. So she would not play Silent.</li>
</ol>
<p><strong>Now consider person B.</strong></p>
<p>Person A is playing Betray.</p>
<ol>
<li>If she continues playing Silent, she gets <span class="math-container">$0$</span>.</li>
<li>If she deviates to Betray, she gets <span class="math-container">$-1$</span>. So she would not play Betray.</li>
</ol>
<p>No player has an incentive to switch strategies. So this is an equilibrium.</p>
<p>The same argument holds for the (Silent, Betray) equilibrium.</p>

CC BY-SA 4.0
2020-11-12T03:53:34.237Z
2020-11-12T03:53:34.237Z
Walrasian Auctioneer
<p>Where would the Nash equilibrium lie in the pictured scenario? Whats confusing me is that both persons best response changes depending on the choice of the other person (there is no dominant strategy). Am I correct in thinking the Nash equilibrium is at (-1,-1) as both A and B want to betray as it would be most beneficial, but as they both betray they end up at (-1,-1)</p>
<p><a href="https://i.sstatic.net/ail4n.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ail4n.png" alt="" /></a></p>

<game-theory><nash-equilibrium><behavioral-economics>
Finding Nash Equilibrium
user888469
# Finding Nash Equilibrium

(Asked by: username_0 on 2020-11-12)

Where would the Nash equilibrium lie in the pictured scenario? Whats confusing me is that both persons best response changes depending on the choice of the other person (there is no dominant strategy). Am I correct in thinking the Nash equilibrium is at (-1,-1) as both A and B want to betray as it would be most beneficial, but as they both betray they end up at (-1,-1)

[![](https://i.sstatic.net/ail4n.png)](https://i.sstatic.net/ail4n.png)

**Tags:** game-theory, nash-equilibrium, behavioral-economics

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## 1 answers

### Answer by username_1 on 2020-11-12. Score: 4 | Accepted answer

The two (pure) Nash equilibrium in this game is (Betray, Silent) and (Silent, Betray).

Let us see why (Betray, Silent) is an equilibrium.

**Let us look at person A.**

Person B is playing Silent.

1. If she plays Betray, she gets $2$.
2. If she deviates to Silent, she gets $1$. So she would not play Silent.

**Now consider person B.**

Person A is playing Betray.

1. If she continues playing Silent, she gets $0$.
2. If she deviates to Betray, she gets $-1$. So she would not play Betray.

No player has an incentive to switch strategies. So this is an equilibrium.

The same argument holds for the (Silent, Betray) equilibrium.


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