Even betweeen nuclear superpowers, there is a Nash competition to field superior conventional forces.

The goal is to achieve escalation dominance, in which your military forces are strongest at all levels of conflict intensity. Think of conflict escalation as a ladder, where the lower rungs are covert or plausibly deniable operations, middle rungs involve conventional war, and the highest rungs involve nuclear war.

All wars involve the escalation of conflict. As a war fighting power, you want to seek dominance not only on the thermonuclear rung, but also on all the rungs below it so that you are not forced into an escalate-or-lose situation. If you achieve escalation dominance on every level, you have achieved hegemony which is a term of art meaning you can compel other powers to act without having to act yourself.

(I leave the proof as an excercise for the reader)