This is just a variation of a very interesting game Douglas Hofstadter describes in Metamagical Themas (extremely highly recommended by the way) in the section on psychological number games. In his game 10 people are allowed to choose "yes" or "no" without knowing what other people chose. If everyone picks "yes" everyone gets $100. If anyone picks "no" then anyone picking "no" gets $10 and everyone else get $0.
He describes inviting 10 of his friends he considers very smart, tells his friends they will be playing with other smart people, then expresses dismay when all his friends pick "no".
My sorry description here doesn't do the story justice. Very worth the time to track down a copy of the book.
This boils down to asking "I'm going to put you in a room with ten peers. Do you believe at least one of your peers will either be irrational, or believe that a peer (possibly you) would be irrational?"
He describes inviting 10 of his friends he considers very smart, tells his friends they will be playing with other smart people, then expresses dismay when all his friends pick "no".
My sorry description here doesn't do the story justice. Very worth the time to track down a copy of the book.