Lets model it.
The left letter will be the red guy and the right letter will be the blue guy. (talking about their moves)
the moves will be pull and nothing.
nothing nothing: 5 points
nothing pull: 5 points + blue death
pull nothing: 5 points + red death
pull pull: 4 points
It would be fun to optimize for most killings and least killings but here you have an interest in your own life.
Suppose you pull, the other person can either pull or not pull. If he pulls then you are alright but if he doesn't you die.
On the other hand, you never die if you just do nothing.
If you do nothing and the other guy pulls then you will 8 people but you are still alive.
Therefore nothing dominates pulling but unfortunately it isn't pareto efficient but you can't always be perfect.
As in most things in life, the best choice is to not do anything.
If you do not care for life then you also do nothing because then you kill at least 5 people but you can upgrade that to 8 if your partner chooses to pull, believing you are a good person and will also pull.
There you get 8 points and get a high score in the local arcade.
(nothing.nothing) will always happen, assuming rational players.