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So, in particular, it can't be a best response
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to the thing being played in the Nash Equilibrium.
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So that's actually a very good proof that proves
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that no strictly dominated strategy
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could ever be played in a Nash Equilibrium.
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But now we have, unfortunately, a little wrinkle,
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and the wrinkle, unfortunately, is weakly dominated, is weak domination.
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So we've argued, it was fairly easy to argue,
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that no strictly dominated strategy is ever going to
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reappear annoyingly in a Nash Equilibrium.
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But unfortunately, the same is not true about weakly dominated strategies.
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And in some sense, you had a foreshadowing of this problem a little bit