Simulating Problems

I suspect that you and I have different concepts of what a simulation is, because you describe an agent (presumably a human being) interacting with the "simulation" in real time. In this case you are mucking up the dynamics of the simulation by introducing a factor which is not accommodated by the model, i.e. the human. The human's reasoning is influenced by knowledge from outside the simulation.

I didn't necessarily mean human agents. For example, this is a simulation of IPD with which non-human agents can interact with. Each step, the agents make decisions based on the current state of the simulation. If you wanted, you could have exactly the same simulation with actual humans anonymously interacting via interface terminals with a server running the simulation. On the other hand, this is a non-simulation of the same problem because it lacks actual agents that would interact with it. It's just a calculation, although an accurate one.

In general, by "simulation" I mean a practical version of a problem that contains elements which would make it impossible or impractical to construct in real life, but is identical in terms of rules, interactions, results, and so on.

Perhaps I am answering a question other than the one you are asking, but: Every exercise in simulation is an exercise in evaluating which modeling concerns are relevant to the system in question, and then accounting for those factors up to a desired level of accuracy.

That is more or less the question I am asking, and evaluating which modeling concerns are relevant to the system in question is the crucial part. But how can we be certain to have made a correct analogy or simplification? It's easy to tell this is not the case if the end results differ, but if those are what we want to learn then we need a different approach.

Is it possible to simulate Omega, for example? Like the mentioned repeated coin toss, except that we would need to prove that our simulation does in fact in all cases lead to the same decisions that an actual Omega would. Or what if we need statistically significant results from a single agent of a one-shot problem, and we can't memory-wipe the agent? Etc.

i'm not sure I understand what you mean by 'failing' in regards to simulations. Could you elaborate?

If you substitute Omega with a repeated toin coss, there is no Omega, and there is no concept of Omega being always right. Instead of repeating the problem, you can also run several instances of the simulation with several agents simultaneously, and only counting those instances in which the prediction matches the decision.

For this simulation, it is completely irrelevant whether the multiple agents are actually identical human beings, as long as their decision-making process is identical (and deterministic).

If anything, I expected to be asked to taboo 'simulation' — by 'problem' I really just mean game theoretical problems such as Newcomb, Prisoner's Dilemma, Iterated Prisoner's Dilemma, Monty Hall, Sleeping Beauty, Two Envelopes, and so forth.

Would tabooing 'problem' really be helpful?

I only used Newcomb as an example to show that determining whether a simulation actually simulates a problem isn't trivial. The issue here is not finding particular simulations for Newcomb or other problems, but the general concept of correctly linking problems to simulations. As I said, it's a rather mathematical issue. Your last statement seems the most relevant one to me:

To simulate Newcomb's problem with a real agent, you have the problem of convincing the agent you can predict his decision, even though in fact you can't.

Can we generalize this to mean "if a problem can't exist in reality, an accurate simulation of it can't exist either" or something along those lines? Can we prove this?