Right, I understand what you mean. I was thinking of in the context of a person being presented with this situation, not an idealized agent running a specific decision theory.
And Omega’s simulated agent would presumably hold all the same information as a person would, and be capable of responding the same way.
Will they? Surely it’s clear that it’s now possible to take $1,001,00, because the circumstances are slightly different.
In the standard Newcomb problem, where Omega predicts your behaviour, it’s not possible to trick it or act other than its expectation. Here, it is.
Is there some basic part of decision theory I’m not accounting for here?
Yes. If the TDT agent picked the $1,001,00 here, then the simulated agent would have two-boxed as well, meaning only box A would be filled.
Remember, the simulated agent was presented with the same problem, so the decision TDT makes here is the same one the simulated agent makes.
Right, I understand what you mean. I was thinking of in the context of a person being presented with this situation, not an idealized agent running a specific decision theory.
And Omega’s simulated agent would presumably hold all the same information as a person would, and be capable of responding the same way.
Cheers for clarifying that for me.