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India and china are below the permafrost lines, even after a WWIII they probably have enough population to constitute 50% of the above worlder population, what tattered government they run would likely be communist, very reminiscent of soviet Russia, rugged equipment, simple, not designed to the rigorous hyper-capitalist standards of the under dwellers, AK 47s with some 2500's attachments. basically, tanks no more potent than old Abrams equivalents.
They are the main foil to the capitalist collective, which runs like a European union, united in ideals, but free to pass their own laws and such. The idea of the nation state has passed, everyone considers themselves a citizen of earth, and sees the communists as barbarians. The corporations foster this one world nation idea, it makes it easier to run things as they aren't bogged down by actually governing stuff, however they compete viciously, private armies and such, they rarely fight directly.
North Africa and south America, as well as northern Australia are the home to pirates and renegades, who neither accept communist rule, or can afford the luxury of the under cities. the climate of these places is similar to northern alaska. 3 or so months of bearable cold 3 or so of cold, and 6 bitter cold months. Piracy is rampant in the Mediterranean and gulf of Mexico, mostly by sea.
The communist power is sovereign, but claims dominance over all above ground, regularly clashing with underworlders. throw some 1984 imagery in there, the corps. aren't afraid of the communists, they like them around, having a constant bad guy to fight keeps people employed, and keeps factories cranking out guns. in a sick perverted sense the corporations are becoming more and more soviet.