A group of friends I'm a part of meet up online on the regular for multiplayer games of Stellaris. It's a fun space Grand Strategy game where you can make your own custom races. One of the options for a custom race is to be a Devouring Swarm type hive mind, much like the Zerg of Star Craft fame or the Tyrannids of 40k. It's not a move normally done in multiplayer games because a devouring swarm really only has one win condition: eat everyone, and most players object to being eaten. In talking about the game with friends it reminded me of some thoughts of PvP in table top RPGs, and what you need for PvP to be a successful part of a game.
Grace in Defeat
Grace in defeat is the easy one that most people pick up on. If someone in your group is a sore loser, the kind of person to make a scene if they get beaten, then you shouldn't have PvP in your game. Ideally you shouldn't have sore losers in your games at all, but I understand that sometimes you can't get ideal traits for all your players and loss in PvE is often easier to take than loss in PvP. At least in PvE the GM isn't bound by the same rules as everyone else.
However, with PvP grace in defeat is important. Why? Because in PvP you can and will lose. It doesn't matter how good you are at it, or how well equipped you are, at some point the dice will turn against you and you will lose. If you can't accept that, then don't engage in PvP.
Grace in Victory
Being a good winner is more important than being a good loser when it comes to PvP. No one likes being lorded over because the dice turned against them. No one wants it rubbed in their face. If you can't just enjoy what happened, without making it out that you're better than the other players, than stay away from PvP.
The real risk with a lack of grace in victory is, well, like I said: eventually you will lose. And when you do lose, if you've been a real dick when you won you can expect people to be a dick back to you. Only they're not going to go with the normal ribbing, they're going to go even harder because you were a dick to them first so they're "just getting you back." And this is how things escalate and how things go out of control.
Enjoyment Is Key
Ultimately you need both for PvP and you need both for everyone involved in PvP. PvP works best when everyone involved knows it is a game, they play to win, but whether they win or lose they can just enjoy how things turned out and what it meant for the story. If someone gets competitive about it, or sulky, salty, or sullen, it can make things awkward. Even worse if someone gets combative over it.
On the plus side, you'll learn pretty quick if your players are the type who can handle it or not. And if they can't, then don't have PvP in the game. Keep things PvE and reap the rewards.