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orthonormal comments on Decision Theory Paradox: PD with Three Implies Chaos? - Less Wrong
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Ah, good.
In retrospect, that remark doesn't apply to multiplayer games; I was thinking of the way that in Newcomb's Problem, the Predictor only cares what you choose and doesn't care about your utility function, so that the only place a TDT agent's utility function enters into its calculation there is at the very last stage, when summing over outcomes. But that's not the case for the Prisoner's Dilemma, it seems.
Right, for TDT agents to expect each other acting identically from the symmetry argument, we need to be able to permute not just places of TDT agents in the game, but also simultaneously places of TDT agents in TDT agents' utility functions without changing the game, which accomodates the difference in agents' utility functions.