There will be no market economy in 2100 as we now know it.
BBR's guide to the world in 2100:
I think any populated regions without strong state control are probably headed for chaos, especially where fertility levels are still high. I would think these regions are also the most likely situations where nuclear weapons could be used. Basically like 1984, but with a rapid onset ice age, and an actual vestige of western civilization remaining in Oceania (although the authoritarian governments are also probably going to be "western"-style remnants outside of China, Japan, and Thailand -- I could see the US re-colonizing most of South America with puppet governments and brute force if need be).
The regions I expect "least change" through 2100 are Oceania, and South America, which is already trending towards fascism (so it has less to lose, lol). Spain, Italy, and the Turks are probably Europe's best bet, and all have historical bents towards strong government. I think Thailand could also be best-positioned out of Asian governments for continuity and stability. Indonesia, India, Pakistan, Iran, most of the Middle East, and Africa are all likely to be destabilized by lack of food, riots, and regional nuclear warfare.
The US may retain a similar population and area but that's only because it will invade Central America and northern South America outright for warmer climes as the situation up north becomes dire. Russia will similarly have to relocate to eastern Siberia, its only region buffered by the Pacific's deep warmth. China should be OK since they are good at purging large %s of their population (historically).
I think this is why the last book from GGRM is not forthcoming. Winter is almost here!