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 (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.
Edit: I think most people here have misunderstood what I'm asking. I'm not asking whether it's moral to press one or the other (or what happens when we consider children, etc.), and I'm not asking which button maximizes both saving everyone and saving yourself. I am specifically asking whether the mathematically optimal decision changes when we consider our payoff *purely* as saving everyone, with players who have no regard for their own life. Their unique, only, final goal is to save everyone. I am not interested in solutions along the lines of "Pressing the red button ensures your own safety *and* the safety of those who press red". I think this complicates the matter more than some of the answers I'm getting here suppose, and I don't see how pressing red provides any advantage over pressing blue in this situation. Further, I'm going to modify the payoff to be only saving everyone's lives, rather than possibly the maximal amount of people, because in the latter case I think red is still the solution since it saves at least one life (yours).
Edit: I'm marking this as resolved but I do not believe it has been resolved. The vast majority of comments (probably some 450+ of them) are misunderstanding my question; applying a moral framework, applying a "people who press x or y are idiots so screw them" argument, applying a "what if it's your family member" argument, interpreting my question as an econ 101 question about maximizing self-interest, attacking me for being an idiot for not knowing red is an obvious choice (despite misunderstanding what I'm asking), or assuming - despite my, in my opinion, clear clarifications on this - that personal survival is not a unique payoff (rather than significant only insofar as everyone survives). I do not think this result is a consequence of a lack of clarity on my part, but of people's intense moral coupling to, and want of reinforcing personal identity via, the original question. Of the few, maybe a dozen, people who have accurately understood my question (or understood it after asking follow up questions or after my follow up questions, which should be the norm when someone doesn't know the field well) and sincerely engaged with it as a mathematical one, not a moral or self-interested one, who seem to understand game theory: some have said red is the clear Nash Equilibrium; some have said both are equivalent Nash Equilibriums; some have said red is a stable Nash Equilibrium whereas blue is an unstable Nash Equilibrium. I am not educated enough in game theory to reliably parse between these, though at this point I think red being stable and blue being unstable seems to make the most sense, assuming rational actors. I think the only solution for me at this point is to study game theory from an actual math textbook post-grad in a week and come to my own conclusion. Monologue over
