‘a’ should use a randomizing device so that he pays 51% of the time and refuses 49% of the time. Omega, aware of this strategy, but presumably unable to hack the randomizing device, achieves the best score by predicting ‘pay’ 100% of the time.
Apply any of the standard fine print for Omega based conterfactuals with respect for people who try to game the system with randomization. Depending on the version that means a payoff of $0, a payoff of 0.51 * $1,000 or an outright punishment for being a nuisance.
Apply any of the standard fine print for Omega based conterfactuals with respect for people who try to game the system with randomization. Depending on the version that means a payoff of $0, a payoff of 0.51 * $1,000 or an outright punishment for being a nuisance.