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.
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.