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Superrationality (or renormalized rationality) is an alternative type of rational decision making different from the widely accepted game-theoretic one, since a superrational player playing against a superrational opponent in a prisoner's dilemma will cooperate while a rationally self-interested player will defect. This decision rule is not a mainstream model within game theory. The concept was created by Douglas Hofstadter, in his article, series, and book ''Metamagical Themas''.〔 – reprinted in: 〕 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. ==Prisoner's dilemma== 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 $101, while the cooperating player gets nothing. The four outcomes and the payoff to each player are listed below One valid way for the players to reason is as follows: # Assuming the other player defects, if I cooperate I get nothing and if I defect I get a dollar. # Assuming the other player cooperates, I get $100 if I cooperate and $101 if I defect. # So whatever the other player does, my payoff is increased by defecting, if only by one dollar. The conclusion is that the rational thing to do is to defect. This type of reasoning defines game-theoretic rationality, and two game-theoretic rational players playing this game both defect and receive a dollar each. Superrationality is an alternative method of reasoning. First, it is assumed that the answer to a symmetric problem will be the same for all the superrational players. Thus the sameness is taken into account ''before'' knowing what the strategy will be. The strategy is found by maximizing the payoff to each player, assuming that they all use the same strategy. Since the superrational player knows that the other superrational player will do the same thing, whatever that might be, there are only two choices for two superrational players. Both will cooperate or both will defect depending on the value of the superrational answer. Thus the two superrational players will both cooperate, since this answer maximizes their payoff. Two superrational players playing this game will each walk away with $100. Note that a superrational player playing against a game-theoretic rational player will defect, since the strategy only assumes that the superrational players will agree. Although standard game theory assumes common knowledge of rationality, it does so in a different way. 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 is one which maximizes payoffs where all the players' strategies are forced to be the same before the maximization step. Some argue that superrationality implies a kind of magical thinking in which each player supposes that his decision to cooperate will cause the other player to cooperate, despite the fact that there is no communication. Hofstadter points out that the concept of "choice" doesn't apply when the player's goal is to figure something out, and that the decision does not cause the other player to cooperate, but rather same logic leads to same answer independent of communication or cause and effect. This debate is over whether it is reasonable for human beings to act in a superrational manner, not over what superrationality means. There is no agreed upon extension of the concept of superrationality to asymmetric games. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Superrationality」の詳細全文を読む スポンサード リンク
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