I love Characteristics of Games so I'm going to quote a section to illustrate some of the pros and cons of playing D&D as a one-sided (multi-player) team game instead of a multi-sided game:Hockey metaphors:
1. The whole team gets the cup.
2. At the very least, you should recognize the assist.
"In and of itself, cooperative interactivity is a good thing, in the sense that interacting with teammates is something many people enjoy--humans are social animals... Also, team interactions introduce all sorts of interesting heuristics (should I pass the ball now, or keep it for myself? should I heal our damage dealer or save my mana to heal our tank later?). But problems can arise when the levels of such interaction are high... problematic cooperative interactivity tends to take the form of socially unpleasant interactions and of role usurpation, both of which we will now discuss.
"In any team game, having good teammates will help you succeed, and bad teammates will hurt your chances. The impact of your teammates on your game experience, however, will vary widely depending on how much cooperative interactive the game has. If the game has very little (e.g. a swim meet), you can still give your best performance regardless of how your teammates perform. Bad performances on their part simply lower the team's overall chances of winning. But if you interact with your teammates a lot, you will be more frustrated if they don't perform well... At an extreme, there are games where a bad teammate is so punishing for the group that you'd rather play a person short than have him on your team... Such games tend to be very hostile to beginners and low-skilled players generally... There is a difference in the emotional experience of being a bad player on a chess team and being a bad player on the football team."
Certainly if you've decided to play hockey as a team, the whole team should get the cup. But if you've decided to play Diplomacy, or Gotcha (a.k.a. Assassin), then forming ad-hoc teams or "parties" doesn't prevent you from still having your own agenda, even while you're playing hockey.