# Non-uniqueness of iterated elimination of weakly dominated strategies?

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?

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 $(D, L)$.