Regarding nuclear brinkmanship, I suspect that a purely rational actor will lose: the nuclear thug will take some, then take some more, and each time the rational actor will acquiesce to avoid nuclear war. This will result in the nuclear thug taking over the world, piece by piece. Ergo, it makes sense to risk nuclear war, or at least convey that you're willing to risk it, because if you don't you lose.
Given the widespread reports during this war of Russian equipment in poor condition, I've been thinking about this possibility for a while:
* Putin fires tactical atomic weapon at some empty plot of Ukrainian land, and announces it as a "demonstration" of Russian might.
* The weapon is a dud.
I'm not sure whether this outcome might not be worse in the long run, in terms of geopolitical stability, than if the weapon performs as expected!
Indeed; Russia was expected to completely flatten all major Ukrainian cities by air in the first day of the war. All those clips of angry Ukrainians jeering nervous Russian troops wouldn't exist if the troops simply gunned down all hostile civilians.
This is also why I am reluctant to call the war "genocide" or a "war crime". They are both terms with pretty specific definitions. Not all wars are genocidal. What Putin and Russian troops are doing is bad enough without misrepresenting their actions.