Yes, all well and good (though I don’t see how you identify any distinction between “properties of the agent” and “decisions . . . predicted to be made by the agent” or why you care about it). My point is that a concept of rationality-as-winning can’t have a definite extension say across the domain of agents, because of the existence of Russell’s-Paradox problems like the one I identified.
This is perfectly robust to the point that weird and seemingly arbitrary properties are rewarded by the game known as the universe. Your proposed redefinition may actually disagree with EY’s theory of Newcomb’s problem. After all, your decision can’t empty box B, since the contents of box B are determinate by the time you make your decision.
Quoting myself:
I’ll go further and say this distinction doesn’t matter unless you assume that Newcomb’s problem is a time paradox or some other kind of backwards causation.
This is all tangential, though, I think.