GAME THEORY¶

GAME THEORY 101 FULL COURSE¶

PROGRESS:¶

The Basics¶

• The Prisoner’s Dilemma and Strict Dominance
• Iterated Elimination of Strictly Dominated Strategies
• Pure Strategy Nash Equilibrium and the Stag Hunt
• What Is a Nash Equilibrium?
• Best Responses
• Matching Pennies and Mixed Strategy Nash Equilibrium
• The Mixed Strategy Algorithm
• How NOT to Write a Mixed Strategy Nash Equilibrium
• Battle of the Sexes
• Calculating Payoffs
• Strict Dominance in Mixed Strategies
• Weak Dominance
• Infinitely Many Equilibria
• The Odd Rule

Extensive Form Games¶

• Subgame Perfect Equilibrium
• Backward Induction
• How NOT to Write a Subgame Perfect Equilibrium
• Multiple Subgame Perfect Equilibria
• Games with Stages
• Punishment Strategies
• Tying Hands (Burning Bridges)
• Commitment Problems
• The Centipede Game
• Problems with Backward Induction
• Forward Induction

Advanced Strategic Form Games¶

• Probability Distributions
• Generalized Battle of the Sexes
• Knife-Edge Equilibria
• Soccer Penalty Kicks
• Comparative Statics
• The Support of Mixed Strategies
• A Trick with Weak Dominance
• Rock Paper Scissors
• Symmetric, Zero Sum Games
• Modified Rock Paper Scissors
• Mixing among Three Strategies

Games with Infinite Strategy Spaces¶

• A Game with No Equilibria
• Duels
• Hotelling’s Game and the Median Voter Theorem
• Second Price Auctions

Expected Utility Theory¶

• Introduction to Expected Utility Theory
• The Completeness Axiom
• The Transitivity Axiom
• Rationality
• Condorcet’s Paradox and Social Preferences
• Lotteries
• Independence over Lotteries
• The Allais Paradox
• The Continuity Axiom
• Expected Utility Transformations
• Pareto Efficiency
• Risk Averse, Risk Neutral, and Risk Acceptant Preferences

Repeated Games¶

• Repeated Prisoner’s Dilemma (Finite)
• Discount Factors
• Geometric Series and Infinite Payoffs
• The One-Shot Deviation Principle
• Grim Trigger in the Repeated Prisoner’s Dilemma
• Tit-for-Tat in the Repeated Prisoner’s Dilemma
• Tit-for-Tat Isn’t Subgame Perfect
• The Folk Theorem
• Repeated Games and the Prediction Problem

Bayesian-Nash Equilibrium¶

• Introduction to Incomplete Information
• Bayesian Nash Equilibrium
• Finding Bayesian Nash Equilibrium with Nash Equilibrium
• Ex Ante and Interim Dominance
• Why Are There Antes in Poker?
• Is More Information Always Better?
• Continuous Types and Cutpoint Strategies
• The Purification Theorem
• Bayes’ Rule
• The Winner’s Curse

Perfect Bayesian Equilibrium¶

• Perfect Bayesian Equilibrium
• Screening Games
• Adverse Selection
• Signaling Games and Updating Beliefs
• Separating Equilibrium
• Pooling Equilibrium
• Off-the-Path Beliefs
• The Beer-Quiche Game
• Semi-Separating/Partially-Pooling Equilibrium