A rational entity can exist in the laws of physics. A rational entity by definition has a determined decision, if there is a rational decision possible. A rational entity cannot make an irrational decision.
You're getting hung up on the determinism. That's not the issue. Rational entities are by definition deterministic.
What they are not is deterministically irrational. Your scenario requires an irrational entity.
Your scenario requires that the entity be able to make an irrational decision, using it's normal thought processes. This requires that it be using irrational thought processes.
It seems you are simply assuming away the problem. Your assumptions:
Then, the described scenario is simply inconsistent, if Omega can use a rational entity as a subject. And so it comes down to which bullet you want to bite. Is it:
A. Rational entities can't exist.
B. Neither choice is irrational.
C. Omega
This is part of a sequence titled "An introduction to decision theory". The previous post was Newcomb's Problem: A problem for Causal Decision Theories
For various reasons I've decided to finish this sequence on a seperate blog. This is principally because there were a large number of people who seemed to feel that this sequence either wasn't up to the Less Wrong standard or felt that it was simply covering ground that had already been covered on Less Wrong.
The decision to post it on another blog rather than simply discontinuing it came down to the fact that other people seemed to feel that the sequence had value. Those people can continue reading it at "The Smoking Lesion: A problem for evidential decision theory".
Alternatively, there is a sequence index available: Less Wrong and decision theory: sequence index