Ok, for something to PvP over, how about adding a few ruined buildings from before the apocalypse? They could be partially functioning, and give some kind of bonus to the owner. They cannot be in safe zones.

An example: you find an abandoned radio station, and it is off the air. You find some generators, and if you can scrounge up some gas, you could start a broadcast. If you do that, then everyone in your tribe gets a bonus. Other tribes will naturally want to take that away and own if for themselves.