[atrifix]

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Again, the goal is not to dominate, it's to maximize utility. It is not rational to have a strategy that does not maximize utility.

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Yes, but our goal is to maximize utility given certain constraints. It can be rational not to play Pareto-optimal strategies, as it is in the one-shot game.
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TFT maximizes utility. If it's one round, then Defecting is the best strategy (well, it's the paradoxical best). Also, the last round of a single game, defecting is best (unless multiple games are going to be played).

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But if you agree with this, then surely you can see that if both players know this, they will also defect in the next to last round? If both players are rational (and know the other is rational), they will both defect in the last round, because they do strictly better. This is true regardless of what happens in the next to last round. Thus the outcome of the next to last round doesn't matter in terms of the last round, because both players will defect at that point. So the players would do strictly better to defect in the next to last round.
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This has been played out in real world multi-game iterative scenarios... TFT won.I guarantee you that if we have a multi-game contest, and I play TFT, and you play All-D, then I will end up with more utility than you (as long as there is at least one other TFT (or non All-D) player. Which, there should be, because if they also play TFT, we will both maximize utility. The only way I don't win, is if everyone else is irrational.

[/ QUOTE ]It's true that TFT won Axelrod's tournaments (I think 7/8), but that doesn't prove that it's rational. First of all, Axelrod's tournament didn't have a definite number of rounds known in advance, so assumption #5 was not applicable. More importantly, consider the one-shot game. If we run tournaments, two players who always cooperate will do strictly better than two players who always defect. But if we agree that defecting is the rational strategy, then the players who cooperate cannot be rational, despite the fact that they beat the other two players. Or, consider this (analagous to Newcomb's problem): a player plays completely at random. His opponent cooperates if and only if an accurate predictor of his actions would have predicted that he would cooperate on that round. Cooperating thus does strictly better than defecting, but do we want to say that random play is rational?