Imagine a multiplayer deathmatch game... Quake 3 will do, although it could be be any kind of competitive deathmatch game. Now throw in a weapon that only triggers when you die, be it accidental death, player kill, team kill or suicide. The weapon will throw you back an arbitrary length of time - say 10 or 15 seconds - back to the same state you were in back then. Time would play forwards from here, you would see your "future" self performing all actions that lead up until your death, as well as all other players, bullets, etc.
Now imagine you could interfere with this. Imagine you could kill the player that killed you. Imagine you could kill yourself before the other player killed you. Imagine you could prevent your death, perhaps by opening the door you needed, or by exploding the trap you were caught in.
We have a paradox on our hands. How would we attempt to resolve it?
If you could shoot bullets into walls in the past, would other players turn around and see the holes? They'd have to, otherwise it wouldn't work. But what if you killed someone in the past - if you killed the player that killed you, where would you reappear? "You" are still in the past, but your "future version" no longer died - would you vanish from the past and appear where you were standing before you "died" and tripped the paradox weapon? How would players perceive this time? Would they see it as real-time, slowed down time, frozen time?
The only way it would truly work in a game is to slow down time or freeze time, else your "future" self would either stand there like a duck, or be taken over by an AI for the "future" that existed after you saved them and then jumped forwards to the "now".
And what if you killed someone in the past - would their paradox weapon fire, sending them back? Could they interact with your past self, or future self, preventing the death of you, thus causing your paradox self to not exist, meaning they never died?
Awww man. My head hurts.