IMO there is a distinction to operate between two types of PC competitiveness/adversity. The first one, which seems to match the three cases you described breaks down to :
- players have secret plans
- the party is supposed to be coherent but every players is ready to give their "in character" behavior first priority at anytime
- players don't seem to openly admit that they're looking for a confrontational style of game with other gamers
The other way would be to be open about this style of play : the GM shouldn't judge, just ask what are players position on the subject, how far may conflict go and still be entertaining, how about players who don'tt care for it ?
From what I understand about D&D players, "let's play an evil characters campaign" means on one hand "let's play bastard badasses" with the freedom to derail the stereotypical goodie two shoes type of adventures. But on the other hand it's an implicit way to say "we want P vs P type of game". Which is fine, except the system doesn't give many guidelines about this, unlike say Paranoia. In my opinion the group must discuss this and maybe define limits to the inner-party adversity. Or maybe the concept of group is ill suited and they should play their characters separately. Problem : one GM might not be enough for a group-less game.
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