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The actual term for this is deterrence — both sides have the nuke, so no one drops first. I can't find a trope by that name; maybe the closest thing is Mexican Standoff?
Edited by Alcor
EDIT: Disregard.
Edited by SpiritOfSahara
@Alcor: Thanks, but I don't think that's it. Both sides had developed the technology independently without the side knowing they had it, but neither used it, in case the other side used it.
I think the example was something to do with detecting weapons, but that seemed too vague.
Both sides have developed better technology, but don't use due to the repercussions of the other side copying it.
One real life example was in WWII.