I don’t know what you are responding to.

I clearly stated that equilibrium is only attainable if everyone has access to nuclear weapons - as in every single sovereign nation - or no one.

I prefer an equilibrium of the latter kind.

I am responding to you, and disagreeing with your claim that the first of your options is a viable long-term equilibrium, contending that that is only true under the degenerate condition of a single sovereignty, otherwise it is a metastable state [0], not a stable long-term equilibrium.

[0] https://www.oxfordreference.com/display/10.1093/oi/authority...

Ah I now see what you mean. I somehow misread your comment as “a single state with nuclear power implies everyone does”. Thanks for clarifying.

That gives you constant empire driven world wars. With those weaker and in danger of getting annexed trying to get nukes desperately.

Maybe consider real humans while evaluating game theory?

I prefer later. As nuclear weapons are the great equalizer. A country with larger conventional army won't be able to bully smaller one... And you really need that sort of capability for equilibrium.