The purpose of this game, admittedly, is to test just how complacent / obedient the Overcoming Bias / Less Wrong community has become.

Think about your assumptions:

First you've got "common rationality". But that's really a smokescreen to hide the fact that you're using a utility function and simply, dearly, hoping that everybody else is using the same one as you!

Your second assumption is that "you gain nothing by defecting alone".

There's no meaningful sense in which you're "winning" if everybody guesses zero and you do too. The only purpose of it, the only reward you receive for guessing 0 and 'winning', is the satisfaction that you dutifully followed instructions and submitted the 'correct' answer according to game theory and the arguments put forth by upper echelons of the Less Wrong community.

In fact, there is much to gain by guessing a non-zero number. First of all, it costs nothing to play. Right away, all of your game theory and rationalization is tossed right out the window. It is of no cost to submit an answer of 100, or even to submit several answers of 100. Your theory of games can't account for this - if people get multiple guesses, submitted from different accounts, you'll be pretty silly with your submission of 0 as an answer.

"But that would be cheating." Well, no. See, the game is a cheat. It's to test "Aumann's agreement theorem" among this community here. It's to test whether or not you will follow instructions and run with the herd, buying into garbage about a 'common rationality' and 'unique solutions', 'utility functions' and such.

You see, for me at least, there's great value in defecting. You of course will try to scare people into believing they're defecting alone, but here you're presupposing the results of the experiment - that everybody else is dutifully following instructions. So anyway, I would be greatly pleased if the result turned out to be a non-zero number. It would restore my faith in this community, actually. And to that end, I would submit a high number...

If I were to play.