If we all take you at your word, that does indeed make it more interesting. If every other entrant acts rationally in choosing P, we must have P = (2/3)(PN + 100)/(N+1), if there are N other participants. This solves to give P = 200/(N+3).
But we don’t know N, we can only guess at it, or some probability distribution of N. N is at least 2, since Psy-Kosh has claimed to have entered, and anyone making this calculation must count themselves among the N. But Psy-Kosh posted before cousin_it revealed its guess of 100, so we might guess that Psy-Kosh voted 0 on the grounds given in the original post, which then modifies the calculation to give P = 200/(N+5).
But suppose of the N non-cousin_it entrants, K entered before knowing cousin_it’s entry, and all chose 0. Then we get P = 200/(N+3+2K).
Now, Aumann agreement only applies if the parties confer to honestly share their information. However, this has been framed as a competitive game, and someone who wants to be the exclusive winner would to better to avoid any such procedure, or to participate in it dishonestly.
A simpler analysis would be to point out that if Psy-Kosh voted zero (as would have been rational without cousin_it), then if everyone else votes zero, all will win except cousin_it. However, if someone votes slightly more than zero, then that one will be the exclusive winner. Someone who values an exclusive win above a tie might try to persuade everyone to vote zero and then defect.
Edit: I have entered, based on the above considerations. My entry was greater than zero.
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.
If we all take you at your word, that does indeed make it more interesting. If every other entrant acts rationally in choosing P, we must have P = (2/3)(PN + 100)/(N+1), if there are N other participants. This solves to give P = 200/(N+3).
But we don’t know N, we can only guess at it, or some probability distribution of N. N is at least 2, since Psy-Kosh has claimed to have entered, and anyone making this calculation must count themselves among the N. But Psy-Kosh posted before cousin_it revealed its guess of 100, so we might guess that Psy-Kosh voted 0 on the grounds given in the original post, which then modifies the calculation to give P = 200/(N+5).
But suppose of the N non-cousin_it entrants, K entered before knowing cousin_it’s entry, and all chose 0. Then we get P = 200/(N+3+2K).
Now, Aumann agreement only applies if the parties confer to honestly share their information. However, this has been framed as a competitive game, and someone who wants to be the exclusive winner would to better to avoid any such procedure, or to participate in it dishonestly.
A simpler analysis would be to point out that if Psy-Kosh voted zero (as would have been rational without cousin_it), then if everyone else votes zero, all will win except cousin_it. However, if someone votes slightly more than zero, then that one will be the exclusive winner. Someone who values an exclusive win above a tie might try to persuade everyone to vote zero and then defect.
Edit: I have entered, based on the above considerations. My entry was greater than zero.
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.