Well, fine, but then the correct strategy depends on Omega’s success rate (and the payoffs). If the reward given to those willing to pay is r, and Omega’s demand is d, and Omega’s prediction success rate is s, the expected payoff for those who agree to pay is s r + (s − 1) d, which may be both positive or negative. (Refusers trivially get 0.)
Omega problems do not (normally) require Omega to be assumed a perfect predictor, just a sufficiently good one.
Well, fine, but then the correct strategy depends on Omega’s success rate (and the payoffs). If the reward given to those willing to pay is r, and Omega’s demand is d, and Omega’s prediction success rate is s, the expected payoff for those who agree to pay is s r + (s − 1) d, which may be both positive or negative. (Refusers trivially get 0.)