Both Korea and Vietnam were test cases for this very issue. In Korea, both China and US backed down from really getting into it (well, China did pretty much what it could). In Vietnam, the same thing: the US was in a tough spot, as the USSR was supplying N. Vietnam, but of course the US could not risk a direct war with the bear.
Let’s hope similar caution keeps India and Pakistan in line. A nuclear war between those two would pretty much guarantee that India does not become a major player in the 21st century.
China and India, and China and Russia, have never gotten along very well. There are areas of conflict between the latter pair, as the Chinese are beginning to leak into Siberia and squat there. China and India will also be vying to become the dominant Asian power, inasmuch as post-war Japan has never tried to dominate militarily/politically, and as its population ages and shrinks its economic power will also diminish.
I think the conflict you see in the Middle East, however, will continue to be the major conflict you’re talking about. That is, I think it’s going to get worse, the US will continue to stay involved, and things will probably not settle down for many more years–perhaps not even until the end of the century.
The culture of the Middle East is starkly incompatible with that of any other in the world. Non-Muslim Asia is extremely secular and has no use for Islam. Western Europe is already in sh*t shape because they have already introduced to many immigrants who have no interest in assimilation. The Americas already have their own kooky religion: Christianity.
The Middle East has oil only. Beyond that, all I see is a region/culture like a 2-year-old child (the terrible twos): nothing but tantrums, whining, and drawing on the walls with crayons. And yes, I include Isreal in that description.
Don’t get me wrong: I have met many Arabs, Iranians, and Muslims from many nations. As individuals, they are very nice people. But there is not a single functional nation in the region. What a mess. They have a lot of growing up to do before they are ready to participate in the world as political “adults.” In the meanwhile, expect more conflict, instability, and terrorism as they take their collective tantrum out on the rest of the world.