Science-fiction writer Jerry Pournelle has a set of stories set in a future where the United States and Russia decide to join together and jointly rule the world
We may even decide to save decadent old eurosclerotic (thank you, Smorch) Europe from itself.
And once we're going strong, India and China will join the party.
As for the Islamic theocracies--they can wither on the vine or blow themselves up or do the shariah or whatever. Who cares?