I know you’re attempting a game theory question here OP, but you’ve got it wrong. There needs to be more outcomes to make it an actual dilemma. Your questions guarantees survival for everyone, with no negative consequences, if everyone presses red. That’s not game theory - it’s just stupid.
Here is a game theory questions.
You and your treasure hunting partner have been separated. There is £50000 of treasure you both found being help hostage. You are given two options
A) Co-operate
B) Betray.
The catches - if you both choose A, then you share the treasure equally and get £25000 each. But if one chooses A and one chooses B, then the person who betrayed their friend (B) gets it all. If both choose B then you only get £1000 each.
Selection options and outcomes:
A - A = each £25000
B - A = B gets £5000 while A gets zero
B - B = each get £1000
That’s a game theory question. Because there are downsides to the “easy” choice. The only way to guarantee that you’ll get something is to betray your friend, because if they choose to cooperate then you win it all, and if they choose to betray then you still get a little something each.
If you choose A, you have the chance to get half the money… but only if your friend also chooses A. It is a risk. If you choose B, you could win it all or you could just get the small amount but at least you get something.
Everyone is better off if you cooperate, but it only works if everyone does it. If one person is greedy and wants it all, then they can choose B and betray. They’ll win it all. That risk makes everyone choose B, so they’ll either win it all or more likely, get a small amount but it’s better than nothing. Betray guarantees you get something, but it will be less than you could have if everyone cooperated.
That’s game theory. Your OP question is not.