The Hunger Games

I would assign priorities with coefficients for the games leading up to the final, for example, green would get 3 points if it forces the red to surrender or kills the red, 2 points for blue, and 1 point for brown, and so on for all colors. This rule would encourage players to randomly distribute themselves before the game and try to eliminate the player who will give them the most points. For example, the system could start not with a full double elimination, but with groups. For instance, if two players with the same faction end up in a game, they might not fight each other because of the points awarded for eliminating certain factions. Something along those lines.