<p>Question from M.W.G-8B4</p>
<p>Show that the order of deletion doesn’t matter for the set of strategies surviving iterated elimination of strictly dominated strategies.</p>
<p>My proof attempt</p>
<p>I assume <span class="math-container">$G_n$</span> the game generated in the n^th step of IDDs.</p>
<p>Suppose <span class="math-container">$s_i^D \in \Sigma_i^n $</span> dominates <span class="math-container">$s_i\in \Sigma_i^n$</span> for given <span class="math-container">$\Sigma_{-i}^n $</span></p>
<p>But let’s assume it is not deleted in this round.</p>
<p>Then at round <span class="math-container">$n+1$</span>, <span class="math-container">$s_i^D \in \Sigma_i^{n+1} $</span> still dominates <span class="math-container">$s_i\in \Sigma_i^{n+1}$</span> for given <span class="math-container">$\Sigma_{-i}^{n+1} $</span></p>
<p>So, the order of deletion doesn’t matter.</p>
<p>— what do you think about my proof attempt? Is this enough to show this statement? Or how can improve this proof?</p>
<p>Any help will be appreciated. Thanks!</p>

CC BY-SA 4.0
2022-10-21T08:18:26.027Z
How can we be sure that $s_i^D$ was not deleted in round $n$? Perhaps it too was strictly dominated?
Giskard
CC BY-SA 4.0
2022-10-21T10:57:40.190Z
Could you please clarify your situation? Are you studying this for an entrance exam? Because I don't think hearing this proof from someone else is useful; it does not use any tricky lemmas or great theorems. So I think that depending on your situation you either do not need to know the proof, or coming up with the proof deepens your understanding. I really don't know any situation where just knowing the proof is useful.
Giskard
<microeconomics><game-theory><self-study>
Show that the order of deletion doesn’t matter for the set of strategies surviving iterated elimination of strictly dominated strategies
studentp
# Show that the order of deletion doesn’t matter for the set of strategies surviving iterated elimination of strictly dominated strategies

(Asked by: username_0 on 2022-10-20)

Question from M.W.G-8B4

Show that the order of deletion doesn’t matter for the set of strategies surviving iterated elimination of strictly dominated strategies.

My proof attempt

I assume $G\_n$ the game generated in the n^th step of IDDs.

Suppose $s\_i^D \in \Sigma\_i^n $ dominates $s\_i\in \Sigma\_i^n$ for given $\Sigma\_{-i}^n $

But let’s assume it is not deleted in this round.

Then at round $n+1$, $s\_i^D \in \Sigma\_i^{n+1} $ still dominates $s\_i\in \Sigma\_i^{n+1}$ for given $\Sigma\_{-i}^{n+1} $

So, the order of deletion doesn’t matter.

— what do you think about my proof attempt? Is this enough to show this statement? Or how can improve this proof?

Any help will be appreciated. Thanks!

**Tags:** microeconomics, game-theory, self-study

> **Comments:**
> **username_1**: How can we be sure that $s_i^D$ was not deleted in round $n$? Perhaps it too was strictly dominated?  
> **username_1**: Could you please clarify your situation? Are you studying this for an entrance exam? Because I don't think hearing this proof from someone else is useful; it does not use any tricky lemmas or great theorems. So I think that depending on your situation you either do not need to know the proof, or coming up with the proof deepens your understanding. I really don't know any situation where just knowing the proof is useful.  

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## 0 answers

