= 27d567bc2d48d9f40e9ccc20ea370b15)
Dagon comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (149)
I've played this game, with an actual small prize to give some incentive in favor of cooperating with the experiment. I was surprised at the number of intelligent-seeming people who did not understand that 0 was the "rational" solution. I was unsurprised at the number of people who understood, and submitted answers they knew were irrational just for fun.
This is a bad test of an agreement theorem. There's no reason to believe that participants are motivated to agree, or that their expression of guess is the same as their belief in the "correct" guess.
Honesty is also a condition for Aumann's agreement theorem, though I neglected to actually ask that people submit only honest guesses.
The Danish newspaper Politiken played this game too, for 5000 kroner. Turns out that the actual answer was 21.6 out of 100.
I agree that it's a pretty flawed test of the agreement theorem, but the real assumption that this game tests is common knowledge of rationality. Only if that holds can we say 0 is the rational solution. If any player does not have that common knowledge, the rational solution is likely to be nonzero.
Did the Politiken game have an explicit policy for what to do in the case of ties? That becomes a more pressing question when kroner are involved.
Best I can tell from Google Translate's version of the page linked in that Wikipedia article, they split the winnings among those who tied at the best guess. The article says that five people guessed the same number and won.
Right. I'm going to guess the smallest number I think no one else will guess to maximize my chances of being the only winner. I don't place any value in winning along with a lot of other people.
<strike>Also, the OP is wrong that the iterated 2/3 process will eventually produce 0. If everyone plays 1, then 2/3 of 1 will round back up to 1.</strike> Edit: Sorry, in a version of this game I once played you were restricted to guessing integers.
2/3 is a valid guess.