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. Douglas Hofstadter (of Scientific American math-column fame) 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:

• Payoffs if both cooperate: (C,C) ⇒ ($6, $6)
• Payoffs if both defect: (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 (repeated PD 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 super-rationality.”

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 (C, C) should be used by both players. This is disastrously bad.

If they know a bit more game theory, they might suggest they use identical mixed strategies — e.g. a 50% chance of C and a 50% chance of D. This will produce the highest payoff on average, of about 50, for each player. So perhaps we should extend SR as follows. If the best symmetric strategy is better than the best asymmetric strategy, use SR. Otherwise…

But we are stuck. If one plays, C, that does not help the other choose D, because the moves are made in secret. 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.

Unfortunately, super-rationality does not make sense. Instead, people win at the prisoners’ dilemma by being irrational in a very human way — they listen to their conscience and play cooperatively (quite often) because it’s the “right thing” to do. Unless, of course, they’ve taken economics. Then they play more “rationally,” and lose.

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.