<p>Consider the game below.</p>

<p>$$
\begin{array}{|r|c|c|}
\hline 
&amp;L&amp;R\\\hline
U&amp;5,1&amp;4,0\\\hline 
M&amp;6,0&amp;3,1\\\hline 
D&amp;6,4&amp;4,4\\\hline
\end{array}
$$</p>

<p>Both $U$ and $M$ are weakly dominated by $D$. </p>

<p>If we start by deleting $U$. This would lead to the removal of $L$ in the next step. Then $M$ would be deleted. The solution would be $(D, R)$.</p>

<p>However, if we start by removing $M$, then $R$ would be removed next, and then $U$. The solution from deleting in this order is $(D, L)$.</p>

CC BY-SA 3.0
2017-10-02T15:46:17.677Z
2017-10-02T15:46:17.677Z
Herr K.
<p>In the lecture, my professor said "when we eliminate weakly dominated strategies, you might end up with different equilibria depending on
the order of deletion!"</p>

<p>Can anyone give me an example?</p>

CC BY-SA 3.0
2017-10-02T11:54:23.207Z
Look at page 2 of http://tuvalu.santafe.edu/~jkchoi/ch2_a.pdf
Michael Greinecker
<game-theory>
Non-uniqueness of iterated elimination of weakly dominated strategies?
Roger
# Non-uniqueness of iterated elimination of weakly dominated strategies?

(Asked by: username_0 on 2017-10-02)

In the lecture, my professor said "when we eliminate weakly dominated strategies, you might end up with different equilibria depending on
the order of deletion!"

Can anyone give me an example?

**Tags:** game-theory

> **Comments:**
> **username_1**: Look at page 2 of http://tuvalu.santafe.edu/~jkchoi/ch2_a.pdf  

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## 1 answers

### Answer by username_2 on 2017-10-02. Score: 1

Consider the game below.

$$
\begin{array}{|r|c|c|}
\hline
&L&R\\\hline
U&5,1&4,0\\\hline
M&6,0&3,1\\\hline
D&6,4&4,4\\\hline
\end{array}
$$

Both $U$ and $M$ are weakly dominated by $D$.

If we start by deleting $U$. This would lead to the removal of $L$ in the next step. Then $M$ would be deleted. The solution would be $(D, R)$.

However, if we start by removing $M$, then $R$ would be removed next, and then $U$. The solution from deleting in this order is $(D, L)$.


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