In economics and game theory, a participant has superrationality (or renormalized rationality) if the participant is perfectly rational (maximizes utility) but assumes that all other participants are also superrational, and that any superrational participant will always come up with the same strategy as any other superrational participant when facing the same problem. Applying this definition, a superrational player in a two player prisoner's dilemma will cooperate while a rationally self-interested player would defect.

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 as an alternative type of rational decision making different from the widely accepted game-theoretic one. Hofstadter provided this definition: "Superrational thinkers, by recursive definition, include in their calculations the fact that they are in a group of superrational thinkers." proposes a decision algorithm which, when executed by a set of agents, will lead to what he called a Perfectly Transparent Equilibrium:

This algorithm can informally be understood as the following sequence of steps:

  1. Determine, given what choices might be available to the players, what outcome would be reached if they each executed the maximin decision rule. Call this outcome .
  2. Eliminate from consideration any outcome that does not Pareto dominate .
  3. Repeat steps 1 and 2 until either there is only one outcome left, or more outcomes are eliminated.

The outcome that survives this elimination process, if any, will be the PTE.

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. Causal decision theory suggests that superrationality is irrational, while evidential decision theory endorses lines of reasoning similar to superrationality and recommends cooperation in a Prisoner's Dilemma against a similar opponent.

Program equilibrium has been proposed as a mechanistic model of superrationality.

See also

  • Evidential decision theory
  • Instrumental convergence
  • Newcomb's problem
  • Perfect rationality
  • Prisoner's dilemma
  • Program equilibrium

References