Repeated games

Definition

Repeated games are strategic interactions that occur multiple times between the same players, allowing them to consider the consequences of their actions over time. This context enables players to build strategies based on past behavior and outcomes, leading to different dynamics compared to one-time interactions. By allowing for cooperation, punishment, and reputation effects, repeated games provide insights into how strategies evolve and how long-term relationships can influence decision-making.

5 Must Know Facts For Your Next Test

1. In repeated games, players can use strategies like tit-for-tat, where they mimic their opponent's previous action, promoting cooperation.
2. The shadow of the future plays a significant role in repeated games, as the prospect of future interactions encourages players to consider long-term benefits over short-term gains.
3. Discounting future payoffs affects player behavior in repeated games; a higher discount factor means players value future payoffs more, promoting cooperative behavior.
4. Reputation is crucial in repeated games; players who consistently cooperate can establish a positive reputation, influencing their opponents' strategies.
5. Repeated games help explain real-world phenomena such as business alliances and international treaties, where ongoing interactions influence strategic decisions.

Review Questions

• How does the concept of the shadow of the future affect strategy choices in repeated games?
  • The shadow of the future refers to how the possibility of future interactions influences current decision-making. In repeated games, this consideration encourages players to cooperate rather than act selfishly since they understand that short-term gains may lead to retaliation in future rounds. This interdependence among moves creates a more complex strategic landscape where players weigh immediate benefits against potential long-term consequences.
• Discuss how strategies like tit-for-tat can promote cooperation in repeated games and the implications this has for strategic interactions.
  • Tit-for-tat is a strategy where a player replicates their opponent's previous move, which can lead to mutual cooperation over time. This strategy works effectively in repeated games because it establishes a clear consequence for betrayal: if one player defects, the other will retaliate in the next round. This reciprocal behavior fosters an environment where cooperation is rewarded and defection is punished, ultimately stabilizing strategies over time and leading to better overall outcomes for both players.
• Evaluate the impact of reputation effects on player behavior and outcomes in repeated games and how this relates to real-world strategic interactions.
  • Reputation effects significantly shape player behavior in repeated games by influencing how current actions are perceived for future interactions. A player who builds a reputation for cooperation may encourage others to do the same, creating an environment conducive to mutual benefit. In real-world situations like business partnerships or diplomatic relations, maintaining a positive reputation can lead to sustained cooperation and successful negotiations. Conversely, a player with a history of defection risks losing trust and being isolated from potential partners, showcasing how critical reputation is for achieving favorable outcomes.

Related terms

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

Cooperative Game: A type of game in which players can form coalitions and negotiate binding agreements to improve their outcomes.

Folk Theorem: A principle that states that in repeated games, a wide range of outcomes can be sustained as Nash equilibria when players are sufficiently patient.