Repeated games

Definition

Repeated games are strategic interactions where the same game is played multiple times, allowing players to consider past actions when making current decisions. This setup can lead to different outcomes compared to a one-time game, as players can develop strategies based on previous interactions and can foster cooperation or competition over time. The dynamics of repeated games highlight the importance of strategy, trust, and potential for long-term relationships among players.

5 Must Know Facts For Your Next Test

1. In repeated games, players have the opportunity to punish or reward each other's past actions, which can sustain cooperation in scenarios like the Prisoner's Dilemma.
2. The concept of subgame perfect equilibrium becomes more relevant in repeated games since players must consider not only the current game's strategies but also future implications of their choices.
3. Strategies like tit-for-tat emerge as effective ways to promote cooperation in repeated games, where a player mimics the opponent's last action.
4. Repeated games can converge on cooperative equilibria, allowing players to achieve better payoffs over time compared to one-shot games.
5. The length of the game repetition and players' discount factors significantly influence the strategies they adopt and the stability of cooperative behavior.

Review Questions

• How does the structure of repeated games affect players' strategies compared to one-time games?
  • In repeated games, the ongoing nature of interactions allows players to adjust their strategies based on previous outcomes, which contrasts with one-time games where players make decisions without regard for future consequences. This ongoing interaction enables strategies that promote cooperation, like tit-for-tat, to emerge, as players can punish uncooperative behavior in future rounds. Consequently, repeated play encourages a focus on long-term benefits rather than immediate gains.
• Evaluate the role of subgame perfect equilibrium in understanding outcomes in repeated games.
  • Subgame perfect equilibrium is crucial in repeated games because it ensures that players’ strategies are optimal at every point in the game, taking into account all possible future scenarios. By considering how each player's strategy will hold up in every subgame, we can predict whether cooperation can be sustained. This concept helps explain why certain cooperative behaviors might develop over time as players learn and adapt their strategies based on past interactions.
• Assess how tit-for-tat strategies can lead to different outcomes in repeated games compared to static strategies in one-shot scenarios.
  • Tit-for-tat strategies can fundamentally change the dynamics of repeated games by fostering an environment of cooperation through reciprocity. Unlike static strategies used in one-shot scenarios that might prioritize individual gains, tit-for-tat encourages players to cooperate by rewarding positive actions and punishing negative ones. This adaptability leads to better overall outcomes for all players involved in repeated interactions, showcasing how strategic flexibility plays a critical role in achieving cooperative equilibria over time.

Related terms

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

Cooperative Game Theory:

A branch of game theory that deals with how players can work together to achieve better outcomes than they would by acting independently.

Prisoner's Dilemma:

A standard example in game theory illustrating how two individuals might not cooperate even if it appears that it is in their best interest.