No. I expect the actual average to be greater than 1. If we did the same thing here, I'd probably pick a value very near 1; there, I picked a value very near 2. After further thought, I now suspect that choice is a bit low.

Certainly, it's true that 0 is the unique fixed point, and it's easy to see this if you think about if for a minute or two. On the other hand, how often do you think it will happen that someone will simply misread the question, and answer something else?

I briefly misread the problem as "pick the guess closest to the average guess;" which is actually a sort of interesting question in itself. (I suspect the answer would be lower than 50, as smaller numbers are actually more mentally available than large numbers.) It was only when I was double-checking the text that I realized I was thinking about the wrong sort of thing. I'm fairly certain that I'm better at catching my own mistakes than most, so I expect this and similar mistakes to actually happen.

If similar misreadings happen even once per 25 respondents, then 1 will probably be closer to the average than 0.

It's not only a schelling point, it's the only correct response if everyone picks it - half of the average of zero is zero.

(This is why I chose 1.)