Nash is great. I normally just teach Prisoner's Dilemma because I think it's easier to understand.
There's a whole body of IR theory related to the "
Nuclear Taboo," as part of the lesson on that (when I used to teach IR), we would talk about who would use nukes, and under which circumstances. Because of the taboo, which first use would almost certainly result in national annihilation, most countries who have them won't use them until or unless there is an existential crisis.
The exception, IMO, is a country like Iran, who would absolutely use them pre-emptively and unapologetically. That's one of the reasons people like Waltz who argue that
allowing Iran to have nukes would somehow make them more responsible are, in this case, idiots.
In related news, we had a couple of meeting with
Jibril Rajoub, a
terrorist Palestinian Authority (PA) senior executive, who specifically said that
he would nuke Israel if he had the capacity. We met with him in Bethlehem, and in Ramallah, years later. When we asked him about this, he refused to walk it back. This is what he had to say in 2013:
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Just as a reminder, Fatah/the PA is the "peaceful alternative" to Hamas.