The secret is to eliminate your opponents, or get other people to eliminate them.
The exception is with assassin games, where you have to eliminate a specific player.
In general, in escalating games, you want to set up a situation where you can eliminate an opponent, and use the spoils you get to eliminate the next, who in turn gives you more spoils to eliminate another players, who gives you more spoils, etcetera.
In Flat rate and no spoils, you want to secure bonusses to guarantee a higher income then your opponents.