You are assuming that all rational strategies are identical and deterministic. In fact, you seem to be using “rational” as a stand-in for “identical”, which reduces this scenario to the twin PD. But imagine a world where everyone makes use of the type of supperrationality you are positing here—basically, everyone assumes people are just like them. Then any one person who switches to a defection strategy would have a huge advantage. Defecting becomes the rational thing to do. Since everybody is rational, everybody switches to defecting—because this is just a standard one-shot PD. You can’t get the benefits of knowing the opponent’s source code unless you know the opponent’s source code.
In this case, I think the rational strategy is identical. If A and B are perfectly rational and have the same preferences, then assuming they didn’t both know the above two, they wold converge on the same strategy.
I believe that for any formal decision problem, a given level of information about that problem, and a given set of preferences, there is only one rational strategy (not a choice, but a strategy. The strategy may suggest a set of choices as opposed to any particular choice), but there is only one such strategy.
I speculate that everyone knows that if a single one of them switched to defect, then all of them would, so I doubt it.
However, I haven’t analysed how RDT works in prisoner dilemma games with n > 2, so I’m not sure.
You are assuming that all rational strategies are identical and deterministic. In fact, you seem to be using “rational” as a stand-in for “identical”, which reduces this scenario to the twin PD. But imagine a world where everyone makes use of the type of supperrationality you are positing here—basically, everyone assumes people are just like them. Then any one person who switches to a defection strategy would have a huge advantage. Defecting becomes the rational thing to do. Since everybody is rational, everybody switches to defecting—because this is just a standard one-shot PD. You can’t get the benefits of knowing the opponent’s source code unless you know the opponent’s source code.
In this case, I think the rational strategy is identical. If A and B are perfectly rational and have the same preferences, then assuming they didn’t both know the above two, they wold converge on the same strategy.
I believe that for any formal decision problem, a given level of information about that problem, and a given set of preferences, there is only one rational strategy (not a choice, but a strategy. The strategy may suggest a set of choices as opposed to any particular choice), but there is only one such strategy.
I speculate that everyone knows that if a single one of them switched to defect, then all of them would, so I doubt it.
However, I haven’t analysed how RDT works in prisoner dilemma games with n > 2, so I’m not sure.