The first section is more or less the standard solution to the open source prisoner’s dilemma, and the same as what you would derive from a logical decision theory approach, though with different and less clear terminology than what is in the literature.
The second section, on application to human players, seems flawed to me (as does the claim that it applies to superintelligences who cannot see each other’s source code).
You claim the following conditions are necessary:
A and B are rational
A and B know each other’s preferences
They are each aware of 1 and 2
But in fact, your concept of predisposing oneself relies explicitly on having access to the other agent’s source code (and them having access to yours). If you know the other agent does not have access to your source code, then it is perfectly rational to predispose yourself to defect, whether or not you predict that the other agent has done the same. Cooperating only makes sense if there’s a logical correlation between your decision to cooperate and your opponent’s decision to cooperate; both of you just being “rational” does not make your decision processes identical.
“Recurrent Decision Theory” is not a meaningful idea to develop based on this post; just read and understand the existing work on UDT/FDT and you will save yourself some trouble.
I want to discuss the predisposition part. My argument for human players depends on this. If I was going to predispose myself, decide to choose an option, then which option would I predispose myself to?
If the two players involved don’t have mutual access to each other’s source code, then how would they pick up on the predisposition? Well, if B is perfectly rational, and has these preferences, then B is for all intents and purposes equivalent to a version of me with these preferences. So I engage in a game with A. Now, because A also knows that I am rational and have these preferences, A* would simulate me simulating him.
This leads to a self referential algorithm which does not compute. Thus, at least one of us must predispose ourselves. Predisposition to defection leads to (D, D), and predisposition to cooperation leads to (C, C).
(C, C) > (D, D) thus the agents predispose themselves to cooperation.
Remember that the agents update their choice based on how they predict the other agent would react to an intermediary decision step. Because they are equally rational, their decision making process is reflected.
Thus A* is a high fidelity prediction of B, and B* is a high fidelity prediction of A.
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.
The first section is more or less the standard solution to the open source prisoner’s dilemma, and the same as what you would derive from a logical decision theory approach, though with different and less clear terminology than what is in the literature.
The second section, on application to human players, seems flawed to me (as does the claim that it applies to superintelligences who cannot see each other’s source code). You claim the following conditions are necessary:
A and B are rational
A and B know each other’s preferences
They are each aware of 1 and 2
But in fact, your concept of predisposing oneself relies explicitly on having access to the other agent’s source code (and them having access to yours). If you know the other agent does not have access to your source code, then it is perfectly rational to predispose yourself to defect, whether or not you predict that the other agent has done the same. Cooperating only makes sense if there’s a logical correlation between your decision to cooperate and your opponent’s decision to cooperate; both of you just being “rational” does not make your decision processes identical.
“Recurrent Decision Theory” is not a meaningful idea to develop based on this post; just read and understand the existing work on UDT/FDT and you will save yourself some trouble.
I want to discuss the predisposition part. My argument for human players depends on this. If I was going to predispose myself, decide to choose an option, then which option would I predispose myself to?
If the two players involved don’t have mutual access to each other’s source code, then how would they pick up on the predisposition? Well, if B is perfectly rational, and has these preferences, then B is for all intents and purposes equivalent to a version of me with these preferences. So I engage in a game with A. Now, because A also knows that I am rational and have these preferences, A* would simulate me simulating him.
This leads to a self referential algorithm which does not compute. Thus, at least one of us must predispose ourselves. Predisposition to defection leads to (D, D), and predisposition to cooperation leads to (C, C). (C, C) > (D, D) thus the agents predispose themselves to cooperation.
Remember that the agents update their choice based on how they predict the other agent would react to an intermediary decision step. Because they are equally rational, their decision making process is reflected.
Thus A* is a high fidelity prediction of B, and B* is a high fidelity prediction of A.
Please take a look at the diagrams.
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.