Superrationality

In economics and game theory, a participant is considered to have superrationality (or renormalized rationality) if they have perfect rationality (and thus maximize their own utility) but assume that all other players are superrational too and that a superrational individual will always come up with the same strategy as any other superrational thinker when facing the same problem. Applying this definition, a superrational player playing against a superrational opponent in a prisoner's dilemma will cooperate while a rationally self-interested player would defect.

This decision rule is not a mainstream model within game theory and was suggested by Douglas Hofstadter in his article, series, and book Metamagical Themas as an alternative type of rational decision making different from the widely accepted game-theoretic one. Superrationality is a form of Immanuel Kant's categorical imperative.

He defined it in a recursive way:

Superrational thinkers, by recursive definition, include in their calculations the fact that they are in a group of superrational thinkers.

Note that contrary to the Homo reciprocans, the superrational thinker will not always play the equilibrium that maximizes the total social utility, and is thus not a philanthropist.

The idea of superrationality is that two logical thinkers analyzing the same problem will think of the same correct answer. For example, if two people who are both good at math and both have been given the same complicated problem to do, both will get the same right answer. In math, knowing that the two answers are going to be the same doesn't change the value of the problem, but in game theory, knowing that the answer will be the same might change the answer itself.

The prisoner's dilemma is usually framed in terms of jail sentences for criminals, but it can be stated equally well with cash prizes instead. Two players are each given the choice to cooperate (C) or to defect (D). The players choose without knowing what the other is going to do. If both cooperate, each will get $100. If they both defect, they each get $1. If one cooperates and the other defects, then the defecting player gets $200, while the cooperating player gets nothing.

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