I disagree. Mutual cooperation need not require preferences inconsistent with the payoff table: it could well be that I would prefer to defect, but I have reason to believe that my opponent’s move will be the same as my own (not via any causal mechanism but via a logical relation, eg if I know they use TDT).
Mutual cooperation need not require preferences inconsistent with the payoff table: it could well be that I would prefer to defect, but I have reason to believe that my opponent’s move will be the same as my own
But the true PD payoff table directly implies, by elimination of dominated strategies, that both players prefer D to C. If a player instead plays C, the alleged payoff table can’t have represented the actual utility the players assigned to different outcomes.
Playing against a TDT user or Omega or a copy of oneself doesn’t so much refute this conclusion as circumvent it. When both players know their opponent’s move must match their own, half of the payoff table’s entries are effectively deleted because the (C, D) & (D, C) outcomes become unreachable, which means the table’s no longer a true PD payoff table (which has four entries). And notice that with only the (C, C) & (D, D) entries left in the table, the (C, C) entry strictly dominates (D, D) for both players; both players now really & truly prefer to cooperate, and there is no lingering preference to defect.
I don’t think it’s using a non-causal decision theory that makes the difference. I could play myself in front of a mirror — so that my so-called opponent’s move is directly caused by mine, and I can think things through in purely causal terms — and my point about the payoff table having only two entries would still apply.
What makes the difference is whether non-game-theoretic considerations circumscribe the feasible set of possible outcomes before the players try to optimize within the feasible set. If I know nothing about my opponent, my feasible set has four outcomes. If my opponent is my mirror image (or a fellow TDT user, or Omega), I know my feasible set has two outcomes, because (C, D) & (D, C) are blocked a priori by the setup of the situation. If two human game theorists face off, they also end up ruling out (C, D) & (D, C), but only in the process of whittling the original feasible set of four possibilities down to the Nash equilibrium.
I disagree. Mutual cooperation need not require preferences inconsistent with the payoff table: it could well be that I would prefer to defect, but I have reason to believe that my opponent’s move will be the same as my own (not via any causal mechanism but via a logical relation, eg if I know they use TDT).
But the true PD payoff table directly implies, by elimination of dominated strategies, that both players prefer D to C. If a player instead plays C, the alleged payoff table can’t have represented the actual utility the players assigned to different outcomes.
Playing against a TDT user or Omega or a copy of oneself doesn’t so much refute this conclusion as circumvent it. When both players know their opponent’s move must match their own, half of the payoff table’s entries are effectively deleted because the (C, D) & (D, C) outcomes become unreachable, which means the table’s no longer a true PD payoff table (which has four entries). And notice that with only the (C, C) & (D, D) entries left in the table, the (C, C) entry strictly dominates (D, D) for both players; both players now really & truly prefer to cooperate, and there is no lingering preference to defect.
TDT players achieving mutual cooperation are playing the same game as causal players in Nash equilibrium.
I’m not sure how you think that the game is different when the players are using non-causal decision theories.
I don’t think it’s using a non-causal decision theory that makes the difference. I could play myself in front of a mirror — so that my so-called opponent’s move is directly caused by mine, and I can think things through in purely causal terms — and my point about the payoff table having only two entries would still apply.
What makes the difference is whether non-game-theoretic considerations circumscribe the feasible set of possible outcomes before the players try to optimize within the feasible set. If I know nothing about my opponent, my feasible set has four outcomes. If my opponent is my mirror image (or a fellow TDT user, or Omega), I know my feasible set has two outcomes, because (C, D) & (D, C) are blocked a priori by the setup of the situation. If two human game theorists face off, they also end up ruling out (C, D) & (D, C), but only in the process of whittling the original feasible set of four possibilities down to the Nash equilibrium.