Omega may be able to predict your reaction without simulating you at all, just like a human may be able to perfectly predict the behavior of a program without executing it
If you perfectly predict something (as Omega supposedly does), you must run a model on some hardware equivalent.
Unless you subscribe to special pleading similar to "if a program does not run on silicon based hardware, it's not truly run" - as Searle does with the special role attributed to the brain - you should expect that model that predicts your reaction to be essentially a simulation of yourself, at least of all components involved in that decision.
Think of it along the lines of brain uploading. To predict your reaction perfectly, someone has to go through your source code on some computational substrate - which means executing it, if only in their "mind". Why privilege certain kinds of Turing Machine implementations?
Omega could tell you "Either I am simulating you to gauge your response, or this is reality and I predicted your response" - and the problem would be essentially the same.
Would it? Being told that, you'd have to immediately assume that there is at least a 50% chance of being a simulation that's going to be switched off after giving your answer - your priorities would change to keep Omega from getting the information it desires off of you. One million currency units versus a 50% chance of ceasing to exist?
Interesting problem, but not essentially the same as the classic Newcomb's.
If you perfectly predict something (as Omega supposedly does), you must run a model on some hardware equivalent.
The less I know about chess, the more certainly I can predict the outcome if I play against a grandmaster.
The only "model" I need is the knowledge that the grandmaster is an expert player and I am not. Where in that am I "running a model"?
Just developing my second idea at the end of my last post. It seems to me that in the Newcomb problem and in the counterfactual mugging, the completely trustworthy Omega lies to a greater or lesser extent.
This is immediately obvious in scenarios where Omega simulates you in order to predict your reaction. In the Newcomb problem, the simulated you is told "I have already made my decision...", which is not true at that point, and in the counterfactual mugging, whenever the coin comes up heads, the simulated you is told "the coin came up tails". And the arguments only go through because these lies are accepted by the simulated you as being true.
If Omega doesn't simulate you, but uses other methods to gauge your reactions, he isn't lying to you per se. But he is estimating your reaction in the hypothetical situation where you were fed untrue information that you believed to be true. And that you believed to be true, specifically because the source is Omega, and Omega is trustworthy.
Doesn't really change much to the arguments here, but it's a thought worth bearing in mind.