= 27d567bc2d48d9f40e9ccc20ea370b15)
GuySrinivasan 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 think it's entirely rational to submit a non-zero answer.
I would prefer to win outright, rather than tie, and I think it's safe to assume this is true of more people than just me.
If everyone does the "rational" thing of guessing 0, it will be a big tie.
If anyone guesses above 0, anyone guessing 0 will be beaten by someone with a guess between 0 and the average.
Therefore, a small non-zero guess would seem superior to a guess of zero, to those who value outright wins above ties (EDIT: and don't value a tie as being much better than a loss).
Perhaps I'll write a program to simulate what the best guess would be if everyone reasons as above and writes a program to simulate it...
The problem is that the game is not well-defined, since we are not told how to value ties. If everyone is allowed to value ties as they please, the game is far more complicated. Instead the OP should say something explicit, and probably it should be "ties are exactly as valuable as wins". But it's hard to enforce that, isn't it?
Yes, because I would continue to prefer to win without a tie. :)
By allowing you to choose a real number rather than just an integer, Warrigal has made it easy to avoid ties. Since I have myself played a non-integer, it is extremely unlikely that anyone will guess the exact value of the answer, so there is no penalty to picking a probably unique real number very close to your actual guess.
EDIT: On second thought, there is a penalty in that you could tie for the right answer with someone else if you chose a salient number, but you would roughly halve your chances of being the winner if you added or subtracted an epsilon.
To improve on in this point, so that it's possible to move either way from anyone else's choice, we could make the choice to be from the open set (0,100) rather than from [0,100]. ;-)