Three player game, standard, sequential.
My thoughts on this are as follows.
If two of the players are weaker than the third and are fairly equall with each other (unable to take the other out) than it pretty much only makes sense to focus on the stronger player together.
Conversely,
If two of the players are dominating the third and are fairly equall with each other than it makes sense to focus on maintaining their dominance, eliminating the weak player and not scuffling with each other.
Obviously there are a million other factors that influence gameplay decisions but all else equall is this where you guys are?
Edit to address post below:
In my second scenario I kind-of meant that the two dominant players sort of just sit on the third wearing him down slowly so that they stay equall with each other. Not just one player burning up all his armies to take out the weak player.