This decision rule is not a mainstream model in game theory and was suggested by Douglas Hofstadter in his article, series, and book Metamagical Themas[1] as an alternative type of rational decision making different from the widely accepted game-theoretic one.
"[1] Unlike the supposed "reciprocating human", the superrational thinker will not always play the equilibrium that maximizes the total social utility and is thus not a philanthropist.
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.
The game-theoretic analysis maximizes payoffs by allowing each player to change strategies independently of the others, even though in the end, it assumes that the answer in a symmetric game will be the same for all.
This is the definition of a game-theoretic Nash equilibrium, which defines a stable strategy as one where no player can improve the payoffs by unilaterally changing course.
The superrational equilibrium in a symmetric game is one where all the players' strategies are forced to be the same before the maximization step.
This debate is over whether it is reasonable for human beings to act in a superrational manner, not over what superrationality means, and is similar to arguments about whether it is reasonable for humans to act in a 'rational' manner, as described by game theory (wherein they can figure out what other players will or have done by asking themselves, what would I do if I was them, and applying backward induction and iterated elimination of dominated strategies).
For simplicity, the foregoing account of superrationality ignored mixed strategies: the possibility that the best choice could be to flip a coin, or more generally to choose different outcomes with some probability.
In a less extreme example, if the payoff for one cooperator and one defector was $400 and $0, respectively, the superrational mixed strategy world be defecting with probability 100/299 or about 1/3.
One example discussed by Hofstadter is the platonia dilemma: an eccentric trillionaire contacts 20 people, and tells them that if one and only one of them send him or her a telegram (assumed to cost nothing) by noon the next day, that person will receive a billion dollars.
The question of whether to cooperate in a one-shot Prisoner's Dilemma in some circumstances has also come up in the decision theory literature sparked by Newcomb's problem.