Game Theory

Game Theory Curriculum

This curriculum provides a structured overview of the study of game theory.

Foundations

Introduction to Game Theory:

• Basic concepts: players, strategies, payoffs
• Types of games: cooperative vs. non-cooperative, static vs. dynamic
• Examples of games: prisoner's dilemma, rock-paper-scissors
• Applications of game theory in various fields

Static Games of Complete Information:

• Normal form representation of games
• Dominant strategies
• Iterated elimination of strictly dominated strategies
• Nash equilibrium: definition and properties
• Finding Nash equilibria in various games

Mixed Strategies:

• Definition of mixed strategies
• Expected payoffs
• Nash equilibrium in mixed strategies
• Existence of Nash equilibria (Nash's Theorem)

Core Concepts

Dynamic Games of Complete Information:

• Extensive form representation of games
• Strategies in dynamic games
• Backward induction
• Subgame perfect Nash equilibrium (SPNE)
• Applications: bargaining, auctions

Static Games of Incomplete Information:

• Bayesian games
• Type spaces and beliefs
• Bayes' Nash equilibrium
• Applications: auctions, signaling

Dynamic Games of Incomplete Information:

• Perfect Bayesian equilibrium (PBE)
• Sequential equilibrium
• Reputation effects
• Applications: repeated games, mechanism design

Further Topics

Cooperative Game Theory:

• Coalitional games
• The core
• Shapley value
• Bargaining solutions

Evolutionary Game Theory:

• Evolutionarily stable strategies (ESS)
• Replicator dynamics
• Applications to biology and social sciences
• Learning in games