It's the prisoners dilemma: best scenario is nobody has nukes. But if your enemy get nukes, you better get them ASAP. A Nash equilibrium is set where everybody should either have nukes or be strongly allied with someone with nukes.

Regarding guns: if you have easy access to weapons, everyone also has access, so the Nash equilibrium is "get a weapon". If weapons circulation is restricted, the Nash equilibrium is "don't waste your money on weapons".