I really enjoy playing Destiny, but I'm getting tired of having to go to external websites (destinylfg) to find fireteams. So, I was thinking about how to incorporate a way to encourage matchmaking without using the auto-match feature and still keeping it within the overall story of the game.
I think a great way would be to create a new room (or open up the upper level permanently) that has different memorial statues or fountains to the fallen guardians. These memorials would be dedicated to the guardians who fell in the 'vault of glass' or those who were lost in the darkness of 'crota's end.' Other statue/fountains could be shrines to the brave souls who took on the prison of elders or heroically gave their light for story or nightfall missions (dramatic prose to be created). PVP might be a little harder to express within the context of the story.
Then if someone is looking for a fireteam for a specific activity, they could find other players congregating around these memorials - allowing for in-game invites. However, it would be important to alert players that they are stepping into a 'fireteam building area' in-game so that new players don't just walk in, look around, and wonder why people are standing around before walking away.
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Or you could add another "Bounty Board" and when you access it, it would display all pending fireteams, what kind of player they want and what activity they are going to play. You could have options to narrow down the list such as class, subclass, light LvL, and other assorted options to streamline the process. If anyone thinks of something else, feel welcome to post below.