In a world where everyone is already either dead or dying, why would you be sick after murdering? There are too many factors to conclude that after murdering someone, the murderer is guaranteed to be upset in the stomach. Serial killers exist, they are sociopaths to the fullest feeling no remorse. You can't assume that your avatar doesn't have any psychological issues, and you can't assume he hasn't already killed once before. There is no back story explaining the breakout just happening. For all you know there have been zombies for the last five to ten years, and your avatar has been struggling to survive having to kill once before. My point is that he could definitely be desensitized to the horrors of taking a life, and thus PvP should stay the way it is. People are selfish creatures, for example you want something in this game to go your way and I don't. A decent way to promote team work should be based upon a skill set. What if when you started you were to pick a profession like mechanic, gun repair, medic, ect... That would promote teamwork, whilst still allowing others to kill and maim who they please.
