Repeated games

Definition

Repeated games are strategic situations where the same game is played multiple times by the same players, allowing for the possibility of strategies to evolve based on past interactions. This framework enables players to build reputations, establish trust, and potentially achieve cooperative outcomes that would not be attainable in a one-shot game. The dynamics of repeated interactions can lead to various equilibria, including the possibility of sustaining cooperation over time.

5 Must Know Facts For Your Next Test

1. In repeated games, players can use past actions to influence future play, making cooperation more feasible compared to one-time interactions.
2. The structure of repeated games allows for the emergence of Folk Theorems, which show that a wide range of payoffs can be sustained as equilibrium outcomes depending on the discount factor.
3. Strategies like tit-for-tat are effective in promoting cooperation by mimicking an opponent's previous action, encouraging mutual cooperation over time.
4. In collusion scenarios, firms can use repeated interactions to sustain higher prices and maximize joint profits through tacit agreements.
5. Understanding beliefs and updating them based on previous rounds is crucial for players to navigate repeated games successfully and achieve desired outcomes.

Review Questions

• How do repeated games allow for the development of cooperation among players who might otherwise choose to defect?
  • Repeated games create an environment where players can build on their history with one another. When players engage repeatedly, they have the chance to establish trust and develop strategies that encourage cooperation. For example, if players adopt strategies like tit-for-tat, they can promote mutual cooperation by responding to each other's previous actions, thus reinforcing cooperative behavior over time. This contrasts sharply with one-shot games where immediate gains from defection might prevail.
• Discuss how Folk Theorems relate to equilibrium payoffs in the context of repeated games and provide an example of how this impacts strategic decisions.
  • Folk Theorems indicate that in repeated games, a multitude of payoff distributions can be sustained as equilibria based on players' strategies and their discount factors. For instance, if players value future payoffs highly, they may find it beneficial to cooperate, knowing that they can achieve better long-term outcomes. This flexibility allows players to strategize around expectations and potential reactions from their opponents, influencing decisions regarding cooperation versus defection.
• Evaluate the implications of beliefs and updating within repeated games on achieving Perfect Bayesian equilibrium among rational players.
  • In repeated games, players continuously update their beliefs based on observed actions from previous rounds. This belief updating is essential for reaching Perfect Bayesian equilibrium because it ensures that all players adjust their strategies according to the latest information available. As rational players observe their opponents' behaviors over time, they can refine their strategies to promote cooperation or deter defection effectively. This dynamic leads to more nuanced interactions where understanding opponents' motivations becomes critical for strategic success.

Related terms

Nash Equilibrium: A situation in which no player can gain an advantage by unilaterally changing their strategy, given that other players' strategies remain constant.

Prisoner's Dilemma: A standard example of a game in which two players may either cooperate or defect; mutual cooperation yields better outcomes than mutual defection.

Trigger Strategy: A strategy used in repeated games where a player cooperates until the opponent defects, after which the player defects indefinitely as a punishment.