In The Hunger Games, Capitol nuked District 13 during the first rebellion of Panem. But, we later learned that District 13 also had nukes, but they didn't use it because it would have meant nobody would have survived.
Now, the question is: How could Capitol even think of using nukes provided Mutual Assured Destruction was in place?
Mutual assured destruction is a doctrine of military strategy and national security policy in which a full-scale use of nuclear weapons by two or more opposing sides would cause the complete annihilation of both the attacker and the defender. It is based on the theory of deterrence, which holds that the threat of using strong weapons against the enemy prevents the enemy's use of those same weapons.
In case Capitol didn't know District 13 had nukes, District 13 could always showed it off to ensure Mutual Assured Destruction was in place.