Hm - I don't know that it's that deep a misunderstanding. If you consider it, giving away the thousand - or clamming up in the Prisoner's Dilemma (http://en.wikipedia.org/wiki/Prisoner's_dilemma), same thing - is a trust-based move, rather than the "rational" one. Remember, if you give away the thousand and they thought you wouldn't, you're left out in the cold. If you didn't have any reason to trust the predictor - if they did no better than chance - you'd have no reason not to keep the thousand.