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.