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We tested how seven LLMs apply four decision theories in a prisoner's dilemma between nearly identical copies. The models largely agreed about CDT and EDT, and all completed policy-FDT trials resulted in cooperation. But their action-FDT recommendations varied dramatically: some models almost always cooperated, while others almost always defected. We then investigated whether requested reasoning effort explained some of this disagreement.
The case of the one-shot prisoners' dilemma between psychological twins is debated in decision theory. Quoting SEP:
One controversial argument that it is rational to cooperate in a PD relies on the observation that my partner in crime is likely to think and act very much like I do... In the extreme case, my accomplice is an exact replica of me who is wired just as I am so that, of necessity, we do the same thing. It would then seem that the only two possible outcomes are where both players cooperate and where both players defect... More generally, even if my accomplice is not a perfect replica, the odds of his cooperating are greater if I cooperate and the odds of his defecting are greater if I defect... The counter argument, of course, is that my action is causally independent of my replica's. Since I can't affect what my accomplice does and since, whatever he does, my payoff is greater if I defect, I should defect.
Conventional wisdom is that causal decision theory (CDT) defects in twin prisoner's dilemma, while evidential decision theory (EDT) cooperates. Realistically, the accomplice will not be a "perfect replica"; there will at least be trivial differences between the prisoners, such as their names, or the look of their prison cell. I use the term "almost-twin prisoner's dilemma / PD" to specify a scenario with minor differences like these.
Functional decision theory (FDT) is a decision theory introduced in a 2017 paper. This paper defines FDT using quasi-causal graphs:
Just as CDT requires that
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