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In game theory, folk theorems are a class of theorems about possible Nash equilibrium payoff profiles in repeated games .〔In mathematics, the term ''folk theorem'' refers generally to any theorem that is believed and discussed, but has not been published. In order that the name of the theorem be more descriptive, Roger Myerson has recommended the phrase ''general feasibility theorem'' in the place of folk theorem for describing theorems which are of this class. See Myerson, Roger B. ''Game Theory, Analysis of conflict'', Cambridge, Harvard University Press (1991)〕 Folk theorems are motivated by a puzzling fact: in many cases, game theory predicts that rational people will act selfishly, since selfishness is the only Nash equilibrium in the game. However, in reality, people act cooperatively. The explanation provided by folk theorems is that, in repeated games, there are many Nash equilibria which are substantially different than in the one-shot game. The fact that the game is repeated allows the players to agree on certain sequences of actions, and punish the players that deviate from that sequence. For example, in the one-shot Prisoner's Dilemma, both players cooperating is not a Nash equilibrium (if at least one of them is rational). The only Nash equilibrium (if both are rational) is given by both players defecting, which is also a mutual minmax profile. One folk theorem says that, in the infinitely repeated version of the game, provided players are sufficiently patient, there is a Nash equilibrium such that both players cooperate on the equilibrium path. == Preliminaries == Any Nash equilibrium payoff in a repeated game must satisfy two properties: 1. Individual rationality (IR): the payoff must weakly dominate the minmax payoff profile of the constituent stage game. I.e, the equilibrium payoff of each player must be at least as large as the minmax payoff of that player. This is because a player achieving less than his minmax payoff always has incentive to deviate by simply playing his minmax strategy at every history. 2. Feasibility: the payoff must be a convex combination of possible payoff profiles of the stage game. This is because the payoff in a repeated game is just a weighted average of payoffs in the basic games. Folk theorems are partially converse claims: they say that, under certain conditions (are different in each folk theorem), ''every'' payoff that is both IR and feasible can be realized as a Nash equilibrium payoff profile in the repeated game. There are various folk theorems, some relate to finitely-repeated games while others relate to infinitely-repeated 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「Folk theorem (game theory)」の詳細全文を読む スポンサード リンク
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