Repeated Game

Background

A repeated game refers to a strategic scenario that is played multiple times by the same participants. The concept is essential in game theory as it highlights how interaction over time influences players’ strategies and outcomes. Unlike single-shot games, repeated games feature a succession of stages where the history of play can impact future decisions.

Historical Context

Repeated games emerged as a powerful concept within game theory, gradually formed during the mid-20th century when mathematicians and economists formalized interactive decision-making processes. The development of repeated games was significantly supported by the works of John Nash and later by the more extensive examination by Robert Aumann and others who provided a deeper exploration into infinite repetitions and strategies.

Definitions and Concepts

• Repeated Game: A strategic game played more than once, possibly infinitely many times where each stage or round is called a period.
• Finite Repetition: The game is played a specific number of times.
• Infinite Repetition: The game is repeated indefinitely.
• Strategy: A plan of action that takes into consideration past actions within the repeated game.
• Nash Equilibrium: A concept where no player can gain by unilaterally changing their strategy, extended across the repeated gameplay.
• Backward Induction: A method used in finite repeated games to determine the equilibrium strategy by analyzing the game from the future to the present.

Major Analytical Frameworks

Classical Economics

Classical economics does not deeply dwell into the intricacies of repeated interactions, focusing more on free markets and self-regulating behavior over singular events.

Neoclassical Economics

Neoclassical economics incorporates game theory through models like Cournot or Bertrand competition, acknowledging how rational agents might adjust strategies based on repetitive interactions.

Keynesian Economics

Keynesian framework does touch upon repeated engagements, especially in labor markets and fiscal policies, where expectations for future periods matter significantly.

Marxian Economics

While strategy may not be a primary focus in Marxian theory, dynamics of repeated economic interactions might be seen in ongoing struggles between classes or entities.

Institutional Economics

Repeated games illustrate how institutions shape and are shaped by ongoing interactions, influencing rules that govern economic behavior.

Behavioral Economics

This discipline deeply investigates strategies adopted in repeated games, demonstrating how actual human behavior often deviates from purely rational predictions due to cognitive biases.

Post-Keynesian Economics

Post-Keynesians consider repeated strategic interactions, primarily in contexts like wage and price setting behaviour in oligopolistic markets.

Austrian Economics

Focuses on individual decision making in dynamic contexts. Repeated games could illustrate how market processes unroll over time according to subjective value judgments.

Development Economics

Investigates how countries or agents adopt long-term strategies when engaging repeatedly over numerous interactions, primarily in growth and cooperation contexts.

Monetarism

Explores the implications of repeated policy implementation by central banks and how it affects credibility and public expectations with economic activity over time.

Comparative Analysis

Repeated games provide a clear comparison against single-shot games by highlighting how the consideration for future interactions influences present behavior. The threat of punishment or promise of reward in future rounds can lead to more cooperation or defection than classical single-game scenarios permit.

Case Studies

1. Price Wars in Oligopolies: Examining repeated competition among companies.
2. Arms Control Agreements: Analyzing repeated diplomacy rounds.
3. Lending and Repayment: In microfinance, study how repeated mutual interaction forms credible expectations.

Suggested Books for Further Studies

1. “Game Theory: Analysis of Conflict” - Roger B. Myerson
2. “Repeated Games and Reputations” - George J. Mailath and Larry Samuelson
3. “An Introduction to Game Theory” - Martin J. Osborne
4. “The Theory of Learning in Games” - Drew Fudenberg and David K. Levine

Related Terms with Definitions

• Nash Equilibrium: A situation where no player can benefit by changing strategies unilaterally.
• Backward Induction: Method of reasoning backward in time, from the end of a problem or scenario to determine optimal actions.
• Folk Theorem: A principle stating that a multitude of outcomes can be sustained in repeated games if players are patient enough.
• Trigger Strategy: A strategy in repeated games where a player’s action depends on past behavior of opponents.