Repeated game

Definition

A repeated game is a strategic scenario in which players engage in the same game multiple times, allowing their previous actions to influence future decisions. This setup enables players to develop strategies based on past interactions, creating opportunities for cooperation or retaliation depending on the behavior of others. The essence of repeated games lies in their ability to sustain cooperative behavior through the threat of future punishment or the promise of future rewards.

5 Must Know Facts For Your Next Test

1. In repeated games, players can use strategies like tit-for-tat, where they mimic the opponent's previous move to encourage cooperation.
2. The threat of future punishment plays a crucial role in maintaining cooperation in repeated games, as it creates an incentive to avoid defection.
3. The Folk Theorem indicates that if players value future payoffs enough, almost any outcome can be achieved as an equilibrium in infinitely repeated games.
4. Repeated games differ from one-shot games because they allow for reputation effects, which can impact how players behave based on past interactions.
5. Factors such as discounting future payoffs and the length of the game can significantly influence the strategies and outcomes in repeated games.

Review Questions

• How does the concept of punishment and reward function within repeated games, and why is it significant?
  • In repeated games, players can enforce cooperation through threats of punishment for defection and promises of rewards for cooperation. This dynamic is significant because it allows players to align their strategies over time. For instance, if one player defects, others might retaliate in subsequent rounds, discouraging future defections. Thus, the ability to influence future behavior based on past actions helps sustain cooperation in ways not possible in one-shot interactions.
• Discuss how the Folk Theorem relates to cooperation among players in repeated games and what assumptions are necessary for its application.
  • The Folk Theorem demonstrates that when a game is played repeatedly and indefinitely, a wide range of cooperative outcomes can emerge as equilibria if players care enough about future payoffs. For this theorem to hold true, several assumptions must be met: players must be patient (i.e., they discount future payoffs at a low rate), the game must be infinitely repeated or sufficiently long, and players must have complete information about each other's past actions. Under these conditions, cooperation becomes sustainable even when individual incentives might lead to defection.
• Evaluate the implications of discounting future payoffs on strategic behavior in repeated games and how it affects long-term cooperation.
  • Discounting future payoffs significantly influences strategic behavior in repeated games because it alters how much weight players place on future consequences compared to immediate gains. When players heavily discount future payoffs, they may prioritize short-term benefits over long-term cooperation, leading to more frequent defections. In contrast, if players value future outcomes highly, they are more likely to cooperate consistently to foster a mutually beneficial environment. This balance between immediate and future incentives is crucial for sustaining cooperation and can determine the overall success or failure of strategic interactions in repeated scenarios.

Related terms

Nash Equilibrium:

A situation in which each player's strategy is optimal given the strategies chosen by other players, leading to a stable outcome where no player has an incentive to deviate.

Subgame Perfect Equilibrium:

An extension of Nash Equilibrium that requires players' strategies to form a Nash Equilibrium in every subgame of the original game.

Folk Theorem:

A result in repeated games that states if the game is repeated indefinitely, a wide variety of outcomes can be supported as equilibria if players are sufficiently patient.