No matter how many people are in the game (as long as it's more than two) you need to establish a source of income. Either by capturing a continent or by getting as many armies on the ground as possible. Either way you want to make it so you're getting as many armies per turn as possible.
Next, when the time is right and you have gained somewhat of an upper hand, you need to strike with all out force. Once everyone realizes that you're doing well, they'll try and rally everyone against you. This will just wear you down to nothing again while someone else takes the lead.
You have to single out the closest or weakest enemy and concentrate all your forces on taking him out. During this time you may take a hit by the other player(s) on the board, but at least you won't have as many fronts to defend and hopefully with a little luck things will progress in your favor.
I never play escalating card games. All the best strategy in the world won't save you when someone with one territory left trades in a set worth a billion armies...just kind of lame.
