Climate negotiations are a sort of prisoner’s dilemma, so we need to find a way to change the game or change the outcome of a prisoner’s dilemma. Hofstadter proposes that if we can induce players to be “super-rational” we may get a more cooperative outcome. Does this make sense?
Hofstadter illustrates super-rationality with the prisoners’ dilemma (PD) game. For example:
- (C,C) ⇒ (6,6)
- (D,D) ⇒ (4,4)
- (C,D) ⇒ (0,10), (D,C) ⇒ (10,0).
Super-rational (SR) players are said to reason that (1) they will both choose the same strategy (in a symmetric game), (2) so they will choose the best among identical strategies. Hence, in the PD game, they consider only (C,C) and (D,D), and both choose C, cooperation, in contradiction to the Nash Equilibrium in which both defect (D).
Hofstadter apparently likes to illustrate this with PD payoff values that give only a slight extra payoff for defection. But the “logic” of his argument is displayed more starkly when applied to the values shown above.
Super-rationality predicts they will both play C and earn $6. But, clearly, a standard player, would defeat a super-rational player $10 to $0. It seems odd that a SR player would not figure this out and decide to use standard rationality. And this should hold even if each knows the other is capable of super-rationality.
What we see here is that it only makes sense to use super-rationality if you know that both you and the other play are required to use it. Otherwise, even if you are capable of super-rationality, and know that your opponent will use super-rationality, you will take advantage of your opponent’s naive belief, and beat the pants off him. And if you are not sure that he will play SR, you will still be glad that you used standard rationality.
Experiments testing PD super games show that players test some strategies, especially in the beginning, and then cooperate quite well until near the end of the super game. Then they tend to defect. It would seem that super rationality would predict that they would be most SR and most cooperative toward the end. If so, super-rationality fails to predict accurately. According to Wikipedia, “Hofstadter failed to obtain experimental results that would lend support to … the concept of superrationality.”
When Super-Rationality Is Not Best
There appears to be an implicit belief among those who discuss super-rationality that it will produce the best outcome. But consider this game:
- (C,C) ⇒ (1,1)
- (D,D) ⇒ (0,0)
- (C,D) ⇒ (74,125), (D,C) ⇒ (125,74)
Super-rationalists will suggest that something very close to a mixed strategy of playing C or D with equal probability should be used by both players. This will produced the highest payoff, of about 50, for each player. But obviously they can both do better if they choose different strategies. So perhaps we should extend SR as follows. If the best symmetric strategy is better than the best asymmetric strategy, use SR. If the reverse is true, use anti-SR. Call this ultra-super-rationality, USR.
But once they decide to use USR, they are stuck. If one plays, C, that does not help the other choose D, even though the other is committed to USR. This is very similar to the root of the SR problem. In the PD game, just because one chooses SR, and strategy C, that does not constrain the other to choose the SR strategy, even if she is fully aware of it.
Super-Rationality and Climate Negotiations.
Climate negotiations begin as a multi-player prisoners’ dilemma — a public goods game. But we would like all the players to feel constrained to act in a “super-rational” matter. We propose to do this in part by getting them to write and sign a treaty in which they agree to select a “common commitment” and abide by it. Super-rationality is (at least in a symmetric game) just a matter of restricting consideration to common commitments — to using the same strategy.
So, shifting negotiations from a focus on individual quantity commitments to a single-price commitment can be seen as an attempt to codify super-rationality. But given the ambiguity of the concept, I would suggest that a price treaty would be better understood as a way to re-enforce helpful irrational tendencies.
The irrationalities that we would like to re-enforce are (somewhat vaguely) conditional cooperation, altruism, and a sense of honor. A common-commitment treaty is likely to support all of these tendencies, but it will still be important to build in as much re-enforcement from self-interest as possible.