Folk theorem (game theory)

Folk theorem (game theory)

infobox equilibrium
name= Folk theorem
subsetof = Minimax, Nash Equilibrium
discoverer = various, notably Ariel Rubinstein
usedfor = Infinitely repeated games
example = Repeated prisoner's dilemma
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 he 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. An early published example is harv|Friedman|1971.

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. [Myerson, Roger B. "Game Theory, Analysis of conflict", Cambridge, Harvard University Press (1991)]

Sketch of proof

A commonly referenced proof of a folk theorem was published in harv|Rubinstein|1979.

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.

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).

On the other hand, MIT economist Franklin Fisher has noted that the folk theorem is not a positive theory.Fisher, Franklin M. "Games Economists Play: A Noncooperative View" The RAND Journal of Economics, Vol. 20, No. 1. (Spring, 1989), pp. 113-124, this particular discussion is on page 118] In considering, for instance, oligopoly behavior, the folk theorem does not tell the economist what firms will do, but rather that cost and demand functions are not sufficient for a general theory of oligopoly, and the economists must include the context within which oligopolies operate in their theory.

References


*.
*
* Mas-Colell, A., Whinston, M and Green, J. (1995) "Micreoconomic Theory", Oxford University Press, New York (readable; suitable for advanced undergraduates.)
* Tirole, J. (1988) "The Theory of Industrial Organization", MIT Press, Cambridge MA (An organized introduction to industrial organization)
* Ratliff, J. (1996). " [http://www.virtualperfection.com/gametheory/5.3.FolkTheoremSampler.1.0.pdf A Folk Theorem Sampler] ". Great introductory notes to the Folk Theorem.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Folk theorem — may refer to:* Ethno cultural studies of mathematics. * Mathematical folklore, theorems that are widely known to mathematicians but cannot be traced back to an individual. * The folk theorem commonly refers to a theorem in game theory that is… …   Wikipedia

  • Core (game theory) — The core is the set of feasible allocations that cannot be improved upon by a subset (a coalition) of the economy s consumers. A coalition is said to improve upon or block a feasible allocation if the members of that coalition are better off… …   Wikipedia

  • Strategy (game theory) — In game theory, a player s strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player s behaviour. A player s strategy will determine the action the player will take at any stage of the… …   Wikipedia

  • Outcome (game theory) — In game theory, an outcome is a set of moves or strategies taken by the players, or their payoffs resulting from the actions or strategies taken by all players. The two are complementary in that, given knowledge of the set of strategies of all… …   Wikipedia

  • Deadlock (game theory) — C D c 1, 1 0, 3 d 3, 0 2, 2 In game theory, Deadlock is a game where the action that is mutually most beneficial is also dominant. (An example payoff matrix for Deadlock is pictured to the right.) This provides a contrast to the Prisoner s… …   Wikipedia

  • Generalized game theory — is an extension of game theory to incorporate social theory concepts such as norm, value, belief, role, social relationship, and institution. The theory was developed by Tom R. Burns and has not had great influence beyond his immediate associates …   Wikipedia

  • Arrow's impossibility theorem — In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives (options), no voting system can convert the ranked preferences of… …   Wikipedia

  • Cooperative game — This article is about a part of game theory. For video gaming, see Cooperative gameplay. For the similar feature in some board games, see cooperative board game In game theory, a cooperative game is a game where groups of players ( coalitions )… …   Wikipedia

  • Chicken (game) — For other uses, see Chicken (disambiguation). The game of chicken, also known as the hawk dove or snowdrift[1] game, is an influential model of conflict for two players in game theory. The principle of the game is that while each player prefers… …   Wikipedia

  • Zero–sum game — For other uses, see Zero sum (disambiguation). In game theory and economic theory, a zero sum game is a mathematical representation of a situation in which a participant s gain (or loss) of utility is exactly balanced by the losses (or gains) of… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”