a) I have successfully moved the average by ~2X compared to if I’d stayed silent.
b) If N is known and everyone acts rationally as you describe, a pair of colluding players can screw everyone over: one guesses 100, the other guesses the new average.
If I may attempt to contribute your brain matter’s outward velocity: When I was contemplating submitting a guess (which I didn’t do), I actually concluded (I have no evidence for this, sorry) that you in particular would probably guess 100. Had I acted on that, the effect would have been nearly the same, except for the possibility that others would be drawing the same inference.
Good, but it’s even more interesting.
a) I have successfully moved the average by ~2X compared to if I’d stayed silent.
b) If N is known and everyone acts rationally as you describe, a pair of colluding players can screw everyone over: one guesses 100, the other guesses the new average.
The combined effect is making my brain explode.
If I may attempt to contribute your brain matter’s outward velocity: When I was contemplating submitting a guess (which I didn’t do), I actually concluded (I have no evidence for this, sorry) that you in particular would probably guess 100. Had I acted on that, the effect would have been nearly the same, except for the possibility that others would be drawing the same inference.