I'm pretty sure that in a fight to the death here, the winner wins if you kill the opponent once.
Even if that's allowed then they can just keep killing him. "Oh, it's that guy Kratos, this will be like your 64th time dying."
Also, Kratos isn't the only character that can come back from the dead. Palutena can keep reviving Pit and Dark Pit(or any humans) if necessary.
Furthermore, IIRC, in the Paper Mario Games, Mario has items that can revive people and Link can use fairies to revive others.
Also, if we allow locations for PS-All Stars to use such as hell, we might as well give Nintendo their afterlife.
In Super Paper Mario, Mario died, and was allowed a(sort-of) free pass back to life. He didn't even need to fight for it.
Of course, they don't need to kill Kratos in order to win.
I doubt Kratos would do much if he's transported to an alternate dimension, chaos controlled into the future or in outer space, has his mind scrambled by Ness, or Shulk doing whatever he wants via the Monados.
Being alone, is my greatest fear.
