I've been thinking about this quite a bit lately, especially due to the DayZ and WarZ debacles; it's a "Shoot-first. Why-ask-questions?" model of game play. Players can survive on their own; other players pose a risk as you can't be certain you can trust them; there's no penalty for killing them; and you gain resources from killing them...in addition to the whole "Now they can't shoot me" thing. I do not find this style of game appealing as-is because there's no mystery as to how the situations pan out: paranoia tends to make those situations predictable. The game design basically supports murdering one another. That said, when camaraderie does take shape in that kind of game, it's fascinating to me...but I don't think it's a good game. It's more of a social experiment.
Perhaps it would be different if co-operation was somehow rewarded (e.g. dungeons/buildings are set so single players cannot possibly conquer them) while killing other players was somehow meaningfully punished: maybe a 'Police Force' (something like CONCORD from EVE Online), or a bounty system, or a HUD widget that would tell you if a given player was a known player-killer. Permanent Death (lose all of your character abilities, gathered equipment and resources, even your character name forever) might work. With Perma-Death a possible consequence, players would be very motivated to try and talk things out first; supported by a bounty system and a way to recognize player-killers immediately, you have a potentially interesting mechanic. (You also have a painfully steep learning curve.) If it's the kind of game that "resets" after a set time period, perhaps players - as they die - could become zombie-fied; I've seen both video games and real-life games do this with some success.
Another way to do it (just off the cuff) would be to have the zombie-equivalent-threat in the game hunt player-killers more aggressively and/or deny them resources and safe havens (forbid them from entering Towns/Player Hubs or whatever): this could, to a degree, balance out with the surplus of resources they would gain from player-killing...but more to the point would (forcibly) engender cooperative play.
If you've ever played the Munchkin card game, that's a reasonable (if cheeky) example of how cooperation with an enemy can be engendered by a game. And there are some very good examples of true co-operative games (e.g. Left 4 Dead) where co-operation is required and working against one another virtually guarantees failure.