“No matter what decision you make, it seems that you will inevitably regret it”—this property depends on the genie being able to predict you. If you break this property, then you are addressing a different scenario.
“It’s not exactly a puzzle that game theory doesn’t always give pure solutions”—interesting comparison, but I don’t see how it is analogous. Even if you implement a probabilistic strategy, you still regret your decision immediately after you make it. In contrast, with impure solutions, you should still endorse the decision right after having made it.
“No matter what decision you make, it seems that you will inevitably regret it”—this property depends on the genie being able to predict you. If you break this property, then you are addressing a different scenario.
“It’s not exactly a puzzle that game theory doesn’t always give pure solutions”—interesting comparison, but I don’t see how it is analogous. Even if you implement a probabilistic strategy, you still regret your decision immediately after you make it. In contrast, with impure solutions, you should still endorse the decision right after having made it.