Philosophy questions - Morality & Moral Theories

[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?

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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?

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Not if 1) they don't know how many rounds are in the game (which is why I disagreed with your #5 assumption earlier), or 2) they will be playing multiple games (thus, making it as if there was no known ending to the game).

[atrifix]

Okay, this is a possible way of solving the paradox. After all, we can reject any of the assumptions, and it seems like in real-life situations information is definitely partial. I don't want to hijack this thread, but I'd argue that there are certain situations where assumption #5 applies that you're still going to want to maintain that it's rational for people to cooperate, so one of the other assumptions must go as well. Consider this quasi-centipede game: on each round, we play a simultaneous-move prisoner's dilemma. Defecting when the other player cooperates pays (5,0), both defecting pays (1,1), and both cooperating adds 3 to each player's payoffs and keeps the game going another round. The game lasts for a finite number of rounds t (say t=3000). Now, if both players cooperate every round, their payoffs are (3004,3004), but in spite of this, there is a unique equilibrium where both players defect on the first round and get (1,1). I suppose that we could maintain that defecting on the first round is the rational play, but that seems pretty counterintuitive.