Nothing in your post or the proceeding discussion is of a “rather mathematical nature”, let alone a precise specification of a mathematical problem.
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.
You do realize that game theory is a branch of mathematics, as is decision theory? That we are trying to prove something here, not by empirical evidence, but by logic and reason alone? What do you think this is, social economics?
Your question is not stated in anything like the standard terminology of game theory and decision theory. It’s also not clear what you are asking on an informal level. What do you mean by “analogous”?
What you have stated is unclear enough that I can’t recognize it as a problem in either game theory or decision theory, and meanwhile you are being very rude. Disincentivizing people who try to help you is not a good way to convince people to help you.
That’s because it’s not strictly speaking a problem in GT/DT, it’s a problem (or meta-problem if you want to call it that) about GT/DT. It’s not “which decision should agent X make”, but “how can we prove that problems A and B are identical.”
Concerning the matter of rudeness, suppose you write a post and however many comments about a mathematical issue, only for someone who doesn’t even read what you write and says he has no idea what you’re talking about to conclude that you’re not talking about mathematics. I find that rude.
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.
You do realize that game theory is a branch of mathematics, as is decision theory? That we are trying to prove something here, not by empirical evidence, but by logic and reason alone? What do you think this is, social economics?
Your question is not stated in anything like the standard terminology of game theory and decision theory. It’s also not clear what you are asking on an informal level. What do you mean by “analogous”?
I’m not surprised you don’t understand what I’m asking when you don’t read what I write.
I did read that. It either doesn’t say anything at all, or else it trivializes the problem when you unpack it.
Also, this is not worth my time. I’m out.
What you have stated is unclear enough that I can’t recognize it as a problem in either game theory or decision theory, and meanwhile you are being very rude. Disincentivizing people who try to help you is not a good way to convince people to help you.
That’s because it’s not strictly speaking a problem in GT/DT, it’s a problem (or meta-problem if you want to call it that) about GT/DT. It’s not “which decision should agent X make”, but “how can we prove that problems A and B are identical.”
Concerning the matter of rudeness, suppose you write a post and however many comments about a mathematical issue, only for someone who doesn’t even read what you write and says he has no idea what you’re talking about to conclude that you’re not talking about mathematics. I find that rude.