In the meantime I fear he is indeed that crazy. He repeatedly stated that his goal is to wipe out Ukraine at any costs. He is a like a little child that doesn't get his way and then blindly hits at everything in his reach.
Russia is desperate to deter EU/USA from involving itself more in the war, and the only way it can do that is by treating to escalate to nuclear war.
But that threat is only effective if people actually think that you will do it, so they must play this so that they seem crazy enough to start a nuclear war.
It's a bit like someone blackmailing you for money for something illegal you did together, only way to get you to pay is to show that they are really willing to expose your secrets, even if they might be exposed also. And once you believe them and start paying they will continue to demand money from you.
What does crazy mean? Irrational? I don’t think so. He is currently following the Nash equilibrium strategy for fighting a war with a non-nuclear power.
Edit: by your terminology I would consider Ukrainians to be crazy. This a good thing and the reason why I’m rooting for them. They’re the underdog. The rational thing for them to do was to capitulate as soon as the invasions started. It takes a “crazy” level of conviction to the do the irrational thing here.
No, capitulation would be irrational, because it would mean they would be controlled and enslaved by Putin. Ukraine has lived under that yoke before, and will do everything possible to prevent it from happening again. There is no surrender possible for them, and that's why Putin cannot possibly win this war.
The only rational response to that would be a nuclear attack on Moscow. Likely, though, he just wants to make you think he’s that crazy. Madness is a major component of MAD.
Indeed. A responsive deterrent is only a deterrent if you believe the other person will absolutely, 100%-of-the-time, without-blinking-an-eye execute the strike.
If you think they might not, because ethics and morals, then the deterrent's value is discounted by your percentage of doubt.
He has a difficult time winning the war already, he’d never be able to win if he pulls in more countries.