Folk Theorem

Definition

The folk theorem is a concept in game theory that suggests that, in repeated games, a wide variety of outcomes can be sustained as Nash equilibria under certain conditions. This means that if players interact multiple times, they can potentially achieve cooperative outcomes that would not be possible in a one-shot game, particularly when there is an infinite horizon and players care about their future payoffs. The folk theorem highlights the importance of establishing trust and reputation over time, as players may adjust their strategies based on past actions.

5 Must Know Facts For Your Next Test

1. The folk theorem applies primarily to infinitely repeated games where players have the opportunity to establish a reputation over time.
2. In an infinitely repeated game setting, players can achieve outcomes like mutual cooperation by using strategies that reward cooperation and punish defection.
3. The folk theorem implies that cooperation can emerge as an equilibrium even when it is not feasible in a single play of the game.
4. Different versions of the folk theorem exist, depending on assumptions about discount factors and the number of players involved.
5. The conditions under which the folk theorem holds include common knowledge among players about the game's structure and their payoffs.

Review Questions

• How does the folk theorem explain the emergence of cooperation in infinitely repeated games?
  • The folk theorem explains that in infinitely repeated games, players can develop strategies that promote cooperation due to the potential for future interactions. Players are more likely to cooperate if they know that future payoffs depend on their current behavior. By establishing trigger strategies or maintaining a reputation for cooperation, players can create incentives that lead to mutually beneficial outcomes, which would not be achievable in a one-shot interaction.
• Discuss the implications of the folk theorem for understanding equilibrium payoffs in repeated games.
  • The folk theorem implies that there is a broader set of equilibrium payoffs available in repeated games compared to one-shot games. Specifically, players can coordinate on cooperative outcomes because they are able to enforce agreements through future retaliation or reward strategies. This shifts the focus from just finding Nash equilibria to considering how past actions influence future decisions, leading to higher overall payoffs than would be possible without the potential for repeated interactions.
• Evaluate how learning models in game theory relate to the folk theorem and its application in dynamic strategic environments.
  • Learning models in game theory are crucial for understanding how players adapt their strategies over time, which complements the insights from the folk theorem. As players gather information about each other’s behavior through repeated interactions, they can adjust their strategies accordingly. This iterative process reinforces cooperative behavior when players recognize mutual benefits from collaboration, aligning with the folk theorem’s assertion that diverse equilibria are possible when players engage repeatedly and consider their long-term outcomes. Ultimately, this connection emphasizes how strategic learning influences stability and cooperation within dynamic environments.

Related terms

Nash Equilibrium:

A situation in a game where no player can benefit by changing their strategy while the other players keep theirs unchanged.

Repeated Games: Games in which the same players interact multiple times, allowing them to build strategies based on previous outcomes.

Trigger Strategies:

Strategies used in repeated games where a player starts with cooperation but reverts to a punishment phase if the other player deviates from cooperation.