There would be eventual competition between all three superpowers. I've said before that each country will play off one another when it is convenient. Friends one day, enemies in another. It's been mentioned here that it will be less ideologically motivated (Capitalism vs. Communism) and more of a type of "Great Game". Japan, however, would be more inclined to have some kind of ideology, since that's what made them a threat OTL (Japanese Supremacy, Divinity Will of the Emperor, etc.) This is almost exactly my viewpoint, too. However, I think the Danish and Dutch would still retain their Caribbean islands. Any thoughts on French Guiana?