In some manner, pursuing a strategy that allows you to end the world allows you to stave off ending the world.

Think of it through the lens of an iterated prisoner's dilemma: if I suddenly develop deathbots and you don't have them, it changes the payoffs for defection/cooperation which could cause me to change strategies and kill you.

I would recommend Axelrod's book "The Evolution of Cooperation" for ideas surrounding this.