Do you press the red or blue button? (Game Theory)

I saw a post recently that stated:

"Everyone in the world has to take a private vote by pressing a red or blue button. If more than 50% of people press the blue button, everyone survives. If less than 50% of people press the blue button, only people who pressed the red button survive. Which button would you press?"

Now, at it's core, I believe this is a moral question and can't be solve via game theory while retaining its original purpose. However, I am interested in the game theoretic approach. From the very little I know about game theory, I believe that if we set a payoff for the players, there exists a Nash equilibrium. Now, it's obvious that if we take the players' payoffs to be to preserve their own lives, then everyone would push the red button since it always guarantees survival.

But, if we take the players' payoffs to be to save everyone, or maybe to save the maximal amount of people (and not to save themselves), is there a clear solution? If everyone presses the red button then everyone survives, but if even one person presses the blue button you fail to attain your payoff. So, is pressing the blue button correct in this situation?

Like I said I know very little about game theory, so I may be incorrect on some points.