People are all over the place but definitely not 50⁄50. The qualitative solution I have will hold no matter how weak the correlation with other people’s choices (for large enough values of N).
If you make the very weak assumption that some nonzero number of participants will choose blue (and you prefer to keep them alive), then this problem becomes much more like a prisoner’s dilemma where the maximum payoff can be reached by coordinating to avoid the Nash equilibrium.
Yes, but if someone accidentally picks blue, that’s their own fault. The blue-picker injures only themselves, hence the stability against trembling hands. I would care enough to warn them against doing that, but I’m not going to quixotically join in with that fault, just so that I can die as well.
Sometimes one must cut the Gordian Knot; there is a clear right answer here, some people are bozos and that is out of my control. It is not a good idea to try and empathize with bozos as you will end up doing all sorts of counterproductive things.
People are all over the place but definitely not 50⁄50. The qualitative solution I have will hold no matter how weak the correlation with other people’s choices (for large enough values of N).
If you make the very weak assumption that some nonzero number of participants will choose blue (and you prefer to keep them alive), then this problem becomes much more like a prisoner’s dilemma where the maximum payoff can be reached by coordinating to avoid the Nash equilibrium.
There is also a moral dimension of not wanting to encourage perverse behaviour
This game has a stable, dominant NE with max reward, just use that
Sure, if you don’t mind the blue-choosers dying then use the stable NE.
There are no blue-choosers in the stable NE, so no, I don’t mind at all about zero people dying.
Doesn’t “trembling hand” mean it’s a stable equilibrium even if there are?
Yes, but if someone accidentally picks blue, that’s their own fault. The blue-picker injures only themselves, hence the stability against trembling hands. I would care enough to warn them against doing that, but I’m not going to quixotically join in with that fault, just so that I can die as well.
well they literally chose it.… maybe they are suicidal?
Your cognitive empathy skills are sorely lacking.
Sometimes one must cut the Gordian Knot; there is a clear right answer here, some people are bozos and that is out of my control. It is not a good idea to try and empathize with bozos as you will end up doing all sorts of counterproductive things.