For example, old and existing game types are the Capture the flag, or king of the hill, or bounty hunter game type, that exist since Sega's the conduit game.
Well, that are my ideas, for aproach new type of games in multiplayer gaming
Victim:
It consist in a gameplay where the first turn is for a one player for be the victim. In this case, when the player is the victim in his turn, he must escape for another players that will try to defeat you. When the turn is lose is turn of victim for another player. The players dont have points for defeat another player that is not the victim in this game type, but have 1 point for defeat the victim in his time turn. When the victim time turn is finish another player have the turn for be the new victim. The victim ever is a different player, the idea is all will be the victim in some time. If you defeat the victim for three times isnt lose one, you can have immunity for one turn.
For a Special Weapon:
It consist, in a game where the player in some time need to capture a special weapon, this weapon is more powerfull than another weapons of the stage. It appears in anywhere. When the player have this weapon, have a easy mode of defeat the adversaries. The weapon have time limit to use it, and you must wait while you defeat to another players, for use it. Only one can use this weapon in same time.