Just a suggestion, they should add a 'Faction Wars' gamemode where it would be a team of 3 or 6 and players will battle with each other depending on what faction they're in. It will only allow you to search for a game if you're wearing a special object from that a certain faction. At the end of the game, players are rewarded +50 to +100 reputation and have a small % chance of getting a piece of gear from your faction (weapon/armor/emblem). I haven't checked if anyone else has created a post like this so sorry if I stole people ideas (: Give more suggestions
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That's kind of what Crucible already is (a Faction War). However I do like the idea as a playlist where FWC and DO can duke it out. I definitely like your idea.