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In game theory, folk theorems are a class of theorems which imply that in repeated games, any outcome is a feasible solution concept, if under that outcome the players' minimax conditions are satisfied. The minimax condition states that a player will minimize the maximum possible loss which they could face in the game. An outcome is said to be feasible if it satisfies this condition for each player of the game. A repeated game is one in which there is not necessarily a final move, but rather, there is a sequence of rounds, during which the player may gather information and choose moves. In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
Minimax (sometimes minmax) is a method in decision theory for minimizing the maximum possible loss. ...
In game theory, the Nash equilibrium (named after John Nash, who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ...
Ariel Rubinstein (born April 13, 1951) is an economist who works in game theory. ...
In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ...
In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ...
Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ...
In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
Minimax (sometimes minmax) is a method in decision theory for minimizing the maximum possible loss. ...
In mathematics, the term folk theorem refers generally to a theorem which 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. As the term is understood by mathematicians, folk mathematics or mathematical folklore means theorems, definitions, proofs, or mathematical facts or techniques that circulate among mathematicians by word-of-mouth but have not appeared in print, either in books or in scholarly journals. ...
Sketch of proof
A commonly referenced proof of a folk theorem was published in 1979 by Ariel Rubinstein.
The method for proving folk theorems is actually quite simple. A grim trigger strategy is a strategy which punishes an opponent for any deviation from some certain behavior. So, all of the players of the game first must have a certain feasible outcome in mind. Then the players need only adhere to an almost grim trigger strategy under which any deviation from the strategy which will bring about the intended outcome is punished to a degree such that any gains made by the deviator on account of the deviation are exactly cancelled out. Thus, there is no advantage to any player for deviating from the course which will bring out the intended, and arbitrary outcome, and the game will proceed in exactly the manner to bring about that outcome. Grim Trigger is a trigger strategy in game theory for a repeated game, such as an iterated prisoners dilemma. ...
A strategy is a long term plan of action designed to achieve a particular goal, as differentiated from tactics or immediate actions with resources at hand. ...
Applications It is possible to apply this class of theorems to a diverse number of fields. An application in anthropology, for example, would be that in a community where all behavior is well known, and where members of the community know that they will continue to have to deal with each other, then any pattern of behavior (traditions, taboos, etc) may be sustained by social norms so long as the individuals of the community are better off remaining in the community than they would be leaving the community (the minimax condition). Anthropology (from the Greek word άνθÏωπος, human or person) consists of the study of humanity (see genus Homo). ...
The word tradition, comes from the Latin word traditio which means to hand down or to hand over. ...
A taboo is a strong social prohibition (or ban) relating to any area of human activity or social custom declared as sacred and forbidden; breaking of the taboo is usually considered objectionable or abhorrent by society. ...
In sociology, a norm, or social norm, is a pattern of behavior expected within a particular society in a given situation. ...
References - Myerson, Roger B. Game Theory, Analysis of conflict, Cambridge, Harvard University Press (1991)
- Rubinstein, Ariel. "Equilibrium in Supergames with the Overtaking Criterion." Journal of Economic Theory 21:1-9
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