That's, by definition, not irrational behavior.

It would be better called "nothing to loose behavior", but of course in the real world that's pretty rare, and certainly does not apply to the politicians in the current situation.

Agreed, if they threaten something like a nuclear bombing. Let's think about another situation: At a family party there is one piece of cake left and 2 people want to eat it. Both people recognise the interest of the other one and try to offer it to the other one, but both now don't try to take it in fear of losing face. In some way you can also apply a chicken game situation here. Or another example: 2 gay men sit in a bar, see each other and consider the other one attractive. They look at each other and smile at each other. But who should make the first step? (Had to take 2 equal partners, with woman and man it is too likely that culture expects the man to act) In both situation neither the price nor the cost is that high, that relatively(!), extrem actions (like being actively impolite, or just sit there and wait in the bar until the other one makes the move) can and should be expected. I'm not into politics that much, that I could give meaningful examples there, but I think according to the situation and threats each party makes, it happens more often then you might think with just these high stakes situations in mind.