I don’t think Newcomb’s Problem can easily be stated as a real (as opposed to a simply logical) problem. Any instance of Newcomb’s problem that you can feasibly construct in the real world it is not a strict one shot problem. I would suggest that optimizing a rational agent for the strictly logical one shot problem one is optimizing for a reality that we don’t exist in.

Even if I am wrong about Newcomb’s problem effectively being an iterated type of problem treating it as if it is seems to solve the dilemma.

Consider this line of reasoning. Omega wants to make the correct prediction. I want Omega to put the million dollars in the box. If I one-box I will either reward Omega for putting the money in the box or punish Omega for not putting the money in the box. Since Omega has a very high success rate I can deduce that Omega puts a high value on making the correct prediction I will therefore put a correspondingly high value on the instrumental value of spending the thousand dollars to influence Omega’s decision. But here’s the thing, this reasoning occurs before Omega even presents you with the problem. It is worked out by Omega running your decision algorithm based on Omega’s scan of your brain. It is effectively the first iteration.

You are then presented with the choice for what is effectively the second time and you deduce that any real Omega (as opposed to some platonic ideal of Omega) does something like the sequence described above in order to generate it’s prediction.

In Charlie’s case you may reason that Charlie either doesn’t care or isn’t able to produce a very accurate prediction and so reason he probably isn’t running your decision algorithm so spending the thousand dollars to try to influence Charlie’s decision has very low instrumental value.

In effect you are not just betting on the probability that the prediction is accurate you are also betting on whether your decision algorithm is affecting the outcome.

I’m not sure how to calculate this but to take a stab at it:

Edit: Removed a misguided attempt at a calculation.