speaking of useful idiots
It would behoove the #3 power to engender mutually damaging discord between #2 and #1. Particularly if it is in a fashion that assures degradation of both rather than any resolution.
Way at the bottom of the food chain I suppose that would manifest as "patriotism" in support of the failed strategies. Both among the Good People and the Charlie Chans.
Which these days basically amounts to ordering a second weiner for the military pageant at the game. Or won ton, probably.