In the event of what you're calling a stalemate, you both lose a point every day, until you're dead. I know it seems harsh, but it pays to have been nice, and not shoot the bits out of everyone else and lose health.
Still, whoever has the most health would end up winning or another stalemate would result. Lose health and just use your med kit to remain stable, or attack with nukes and whoever has more health auto wins.
The game mechanics are flawed and all strategic value is lost at the endgame.