[Question] Mutual Assured Destruction used against AGI

So I googled and didn’t find a related topic in such terms. Suppose we put a few astronauts on an asteroid, no regular contact with Earth. The moment they detect the light on Earth has blinked out, they send a projectile of Gray Goo to the Earth to stop the AGI from completing whatever its assigned end goal. If MAD has kept us humans in check, surely it’d work on more rational agents?

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