So after some discussion I've decided to set my Skirmish RPG in a setting which is essentially a company, for the moment dubbed AlterniTech, exploiting parallel Earth's. When I was getting a feel for the game I instantly added Alternative AlterniTech's from other Earth's doing the same thing you are.
Then it came to my attention, this is an RPG with a GM. A GM can run simultaneous campaigns for different people in the same game, this setting makes it entirely possible for those to happen literally in the same multiverse without needing to cross over. Of course the very nature of the game is that you're out to profit from others, so why not profit from the GM's other AlterniTech?
What I am asking really, do you feel that I should account for PvP, having one group literally raid another's and having them fight over control of assets?(For example there is a unique weapon in the game which due to balancing reasons can't be developed by the players BUT there is the option for a GM to make ONE available to be captured per campaign, now if two groups have captured their one but they want more, it is perfectly explainable for a group to raid the others for theirs...I'm sure the other group won't just hand it over though so the risk of casualties to undertake the operation balances out the reward)
More importantly, would you ENJOY fighting other players who are also you?
If you want to play a game with winners and losers, then play a board game. Once the game is finished, it's all over and you can play a new game, with everyone starting equal again. I love board games and am glad to play them. But if that's what you want to do, call it that and choose good board games; don't turn your RPG into a bad board game.
As a GM, if the player-characters are fighting each other, it's a sign that the challenges that they are facing are not tough enough. My goal is to present them with challenges that they can only complete by working together and being smart. This gives them a true feeling of camaraderie and accomplishment, which, to me, is the goal of an RPG.
One important aspect of the game is that characters are actually expected to die...a lot. The character creation is streamlined so a player can replace their character well within time to hop in. Gameplay is broken into segments, it makes dropping in and out easier, if that's due to character death of player unavailability it doesn't matter.
Really this is a board game with roleplay aspects added on, a group of players isn't expected to fight amongst themselves. In fact the rules explicitly make it impossible with offensive abilities stating "target hostile". However within the lore and setting it occurred, two different groups can fight. In fact players aside, the entity the players represent have NPC equivalents that the GM could use to the same end.
Sort of like if a GM ran a wednesday and saturday group, and then one day they were both free on a friday. I found the idea of competition between two campaigns quite interesting, and I already had rules for NPC equivalents of the players to get involved when the idea of PvP began to develop.
The game itself is about loss, and recovering from it. From the offset you are in charge of an almost bankrupt company using their only remaining patent to make money. Characters are expendable entities, of course dying isn't impact free because any XP you gained will be lost. That said XP gain is limited anyway, the highest reward being 2 XP and that's for killing upwards of 7 or so enemies and the rewards from earning it are insignificant in terms of day to day. Items themselves are recoverable from a dead character with no penalty, I'd say I'd failed as a designer if the same characters who started the campaign finished it.