**Folk Theorem**
**Definition**
A folk theorem is a concept in game theory that describes a set of equilibrium outcomes in repeated games, showing that a wide range of payoff profiles can be sustained as equilibrium if players are sufficiently patient.
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**Folk Theorem**
In game theory, the folk theorem refers to a collection of results that characterize the possible equilibrium payoffs in infinitely repeated games. These theorems demonstrate that if players interact repeatedly over an indefinite period and value future payoffs highly enough, then many outcomes, including those that are not equilibria in one-shot games, can be sustained as equilibrium outcomes through appropriate strategies.
### Background and Significance
The term „folk theorem” arises because these results were initially known informally among researchers before being formally proven. The theorems highlight the power of repeated interaction in enabling cooperation and enforcing mutually beneficial outcomes, even in games where short-term incentives might lead to defection or non-cooperation.
### Key Concepts
– **Repeated Games:** Games played multiple times by the same players.
– **Equilibrium Payoffs:** Outcomes where no player can improve their payoff by unilaterally changing their strategy.
– **Patience:** Players must value future payoffs sufficiently to maintain cooperation.
### Applications
Folk theorems have applications in economics, political science, and evolutionary biology, providing insight into how cooperation can emerge and be sustained in competitive environments.
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**Meta Description**
The folk theorem in game theory explains how a wide range of outcomes can be sustained as equilibria in repeated games when players are patient. It highlights the role of repeated interaction in fostering cooperation.