What you are talking about its the hypothesis of mutually assured destruction. while the USSR and the USA never went into full scale nuclear war, they did both escalate their arms and came dangerously close too many time. Honestly the logic of having a bigger stockpile to rpevent your neighbor from attacking you is fundamentally flawed. More over there is nothing to say that the amassment of arms on either side is what prevented nuclear warfare. It could have been (and more likely was) any number of other factoers including economic pressure, the UN, frnce, oil negotiations, iran, chinese economic instability. etc...