It's not the antagonistic tone of your comments that puts me off, it's the way in which you seem to deliberately not understand things. For example my definition of analogous — what else could you possibly have expected in this context? No, don't answer that.

I genuinely don't understand what question you're asking

I believe I have said everything already, but I'll put it in a slightly different way:

Given a problem A, find an analogous problem B with the same payoff matrix for which it can be proven that any possible agent will make analogous decisions, or prove that such a problem B cannot exist.

For instance, how can we find a problem that is analogous to Newcomb, but without Omega? I have described such an analogous problem in my top-level post and demonstrated how CDT agents will in the initial state not make the analogous decision. What we're looking for is a problem in which any imaginable agent would, and we can prove it. If we believe that such a problem cannot exist without Omega, how can we prove that?

The meaning of analogous should be very clear by now. Screw practical and impractical.

As an aside note, I don't know what kind of stuff they teach at US grad schools, but what's of help here is familiarity with methods of proof and a mathematical mindset rather than mathematical knowledge, except some basic game theory and decision theory. As far as I know, what I'm trying to do here is uncharted territory.