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Recommended Course Outline for Advanced Game Theory

This recommended course outline is an ordered list of topics and lecture videos that I follow in my graduate level game theory courses. Watching lecture videos in my channel with a proper order is key for effective learning because the concepts in each video is built over the ones that I introduce in previous videos.

 

Course Description and Objective

This course is a graduate level introduction to game theory and strategic thinking. It introduces the theory of cooperative and non-cooperative games with emphasis on economic applications. Game theory is the study of multi-person decision problems where action of each decision maker (player) may influence payoffs of others. In such environments, optimal decision requires strategic thinking; how one’s action will influence the incentives of other players and whether others are aware of this interconnection. 

 

Success in this course requires strong analytical and logical thinking and the habit of drawing conclusions based on qualitative information. The course requires a working knowledge of propositional logic, calculus (e.g., functions of one or several variables, derivatives), probability (e.g., random variables, probability distributions, conditional probabilities, expectations) and optimization.

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Some of the topics covered in the class will be familiar to you from undergraduate or previous studies, but they will be treated in greater depth. At the end of the course, students should be able to 

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  • formulate any strategic interaction as a game form,

  • understand solution concepts in cooperative and non-cooperative games (whether it is in strategic or extensive form), and 

  • develop analytical and problem-solving skills to analyze games.

Suggested Textbooks

"Game Theory” by Drew Fudenberg and Jean Tirole.

“Microeconomic Theory” by Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green.

“A Course in Game Theory” by Martin Osborne and Ariel Rubinstein.

“Strategy: An introduction to Game Theory” by Joel Watson.

Course Outline

 

TOPIC 1: BASICS OF NON-COOPERATIVE GAME THEORY: STRATEGIC - FORM GAMES WITH COMPLETE INFORMATION

 

  1. Strategic (normal) form games 

  2. Pure Strategies

  3. Mixed Strategies

  4. Competitive and zero-sum games

  5. Minimax and maximin values

  6. Minimax Theorem

  7. Dominant and dominated strategy, dominant strategy equilibrium

  8. Iterated elimination of strictly dominated strategies

  9. Best response

  10. Nash Equilibrium and existence theorems

  11. Second Price Auction: The Game

  12. Solving Second Price Auction: An Equilibrium

  13. Solving Second Price Auction: All equilibrium

  14. Nash Demand Game: The Game

  15. Solving Nash Demand Game: All Equilibrium

  16. Second Price Auction with Complete Information: The Game

  17. Solving Second Price Auction  with Complete Information:  An Equilibrium

  18. Solving Second Price Auction with Complete Information: All Equilibrium

  19. Nash Demand Game: The Game

  20. Solving Nash Demand Game with Outside Option: All Equilibrium

  21. Proof of Nash Theorem

  22. Never Best Response, IESDS, and IEWDS

  23. Rationalizability

  24. Correlated Equilibrium

TOPIC 2: BASICS OF NON-COOPERATIVE GAME THEORY: EXTENSIVE FORM GAMES WITH COMPLETE INFORMATION

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  1. Describing extensive form games: Part 1 (Histories)

  2. Describing extensive form games: Part 2 (Player functions and information sets)

  3. Describing extensive form games: Part 3 (An example)

  4. Pure strategies in extensive form games

  5. Payoff calculations of pure strategies

  6. Mixed and behavioral strategies

  7. Payoff calculations of mixed strategies

  8. Payoff calculations of behavioral strategies

  9. Nash equilibrium of extensive form games

  10. Continuation games of extensive Form games 

  11. Continuation Strategies and payoffs

  12. Subgames 

  13. Subgame perfect Nash equilibrium

  14. Games with Perfect Recall : Equivalence of Mixed and Behavioral Strategies 

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TOPIC 3: SOLVING EXTENSIVE FORM GAMES - APPLICATIONS 

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  1. How to find Subgame Perfect Nash equilibrium of Simple Games: Backward Induction

  2. How to find Subgame Perfect Nash equilibrium of Simple Games with Imperfect Information

  3. One Deviation Property

  4. One Deviation Property: An Example

  5. War of Attrition Game and its Solution in Pure Strategies

  6. War of Attrition Game and its Solution in Mixed Strategies

  7. Rubinstein' Alternating Offer Bargaining Game and its Solution for the Two-Period Version

  8. Rubinstein's Alternating Offer Bargaining Game and its Solution for the Infinite Horizon Version

  9. Repeated Games

  10. Finding Subgame Perfect Nash Equilibrium of a Finite Horizon Repeated Game: An Example

  11. Infinitely Repeated Bertrand Competition: Collusion and Monopoly Pricing

  12. Folk Theorem

  13. Finding Nash Equilibrium of an Extensive Game with Imperfect Information: An Example

  14. Robustness of Equilibrium Under Affine Payoff Transformations

  15. Supporting Non Nash Payoffs in Repeated Games

  16. Why is One-Shot Deviation Property Correct and the Key for Calculating SPNE

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TOPIC 4: INTRODUCTION TO COOPERATIVE GAME THEORY AND ITS SOLUTION CONCEPTS 

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  1. Cooperative Game Theory: Some Examples

  2. Cooperative versus Noncooperative Game Theory

  3. Coalitional Games

  4. Outcome of a Coalitional Game

  5. Superadditive Games

  6. Stability

  7. Core

  8. Epsilon Core

  9. Stability and Fairness

  10. Shapley Value

  11. Calculating Shapley Values: An Example

  12. Axiomatization of Shapley Value

  13. Some Positive Results

  14. Alternative Solution Concept: Banzhaf Index

  15. Alternative Solution Concept: Nucleolus

  16. Alternative Solution Concept: Kernel

  17. Solving for Core: Cooperative Voting Game

  18. Some Remarks on Epsilon Core: Cooperative Voting Game

  19. Simple Games with No Veto Player: Cooperative Voting Game

  20. Solving for Shapley Value: Cooperative Voting Game

  21. Solving for Kernel: Cooperative Voting Game

  22. Solving for Nucleolus: Cooperative Voting Game

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TOPIC 5: COOPERATIVE (NASH) BARGAINING 

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  1. Cooperative (Nash) Bargaining Problem: The Framework​

  2. Cooperative (Nash) Bargaining Problem: An Example

  3. Pareto, Weak Pareto, and Individually Rational Sets of Bargaining Problems

  4. Bargaining Rules for Cooperative (Nash) Bargaining Problems

  5. Cooperative Bargaining Axioms: Pareto Optimality and Symmetry

  6. Cooperative Bargaining Axioms: Scale Invariance

  7. Cooperative Bargaining Axioms: Independence of Irrelevant Alternatives (IIA)

  8. Nash Theorem and Nash Bargaining Rule

  9. Pareto Optimality and Nash Bargaining Rule

  10. Symmetry and Nash Bargaining Rule

  11. Independence of Irrelevant Alternatives (IIA) and Nash Bargaining Rule

  12. Scale Invariance and Nash Bargaining Rule

  13. Solving for Nash Bargaining Outcome: Two Examples

  14. Weighted Nash Bargaining Rule

  15. Kalai-Smorodinsky Bargaining Rule

  16. Kalai-Smorodinsky Theorem

  17. Solving for Kalai Smorodinsky Bargaining Outcome: Two Examples

  18. Egalitarian Bargaining Rule

  19. Bargaining Axioms: Translation Invariance and Strong Monotonicity

  20. Utilitarian Bargaining Rule

  21. Calculating Egalitarian Rule Bargaining Solution: A numerical Example

  22. Egalitarian Rule Satisfies Strong Monotonicity

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TOPIC 6: BANKRUPTCY (CLAIMS) PROBLEM 

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  1. Bankruptcy (Claim) Problems and Division Rules

  2. Respect of Minimal Rights Property

  3. Equal Treatment of Equals Property

  4. Claim Monotonicity Property

  5. Resource Monotonicity Property

  6. Proportional Rule and Its Properties

  7. Constrained Equal Awards Rule and Its Properties

  8. Constrained Egalitarian Rule and Its Properties

  9. Constrained Equal Losses Rule and Its Properties

  10. Constrained Equal Awards Rule Satisfies Claims Monotonicty

  11. Constrained Egalitarian Rule Satisfies Claims Monotonicity

 

TOPIC 7: MATCHING THEORY 

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  1. Centralized versus Decentralized Markets

  2. A Simple Theory of Matching: Gale and Shapley's One-to-One Matching

  3. Stable One-to-One Matching

  4. Deferred Acceptance Algorithm (One-to-One Matching)

  5. Manipulability of a Matching Mechanism: Strategy-Proofness

  6. Strategy-Proof and Stable Mechanisms for One-to-One Matching

  7. House Allocation Problem

  8. Serial Dictatorship Mechanism

  9. Housing Market: A Pure Exchange Economy

  10. Top Trading Cycle Mechanism: How it works?

  11. Top Trading Cycle Mechanism: Properties

  12. House Allocation With Existing Tenants

  13. You Ask (Request) My House - I get Your Turn (YRMH-IGYT) Algorithm: A Numerical Example

 

TOPIC 8: VOTING 

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  1. Voting

  2. Voting: Plurality Rule

  3. Run-off Voting

  4. Voting: Majority Rule

  5. Rank Order Voting (Borda Count)

  6. Ordinal versus Cardinal Voting Rules

  7. Voting: The Model

  8. Voting Axioms: Pareto Principle (P)

  9. Voting Axioms: Anonymity (A)

  10. Voting Axioms: Neutrality (N)

  11. Voting Axioms: Independence of Irrelevant Alternatives (IIA)

  12. Voting Axioms: Ordinality (O)

  13. Voting Axioms: Decisiveness (D)

  14. Arrow's Impossibility Theorem and Condorcet Paradox (Cycles)

  15. Strategic Voting

  16. Strategic Voting: Gibbard-Satterthwaite Impossibility Theorem

 

TOPIC 9: BAYESIAN GAMES AND BAYESIAN NASH EQUILIBRIUM 

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  1. Introduction to Bayesian Games 

  2. Bayesian Games and Bayesian Nash Equilibrium (BNE) 

  3. An Example for Bayesian Nash Equilibrium 

  4. An Example for Bayesian Nash Equilibrium 

  5. An Example for Bayesian Nash Equilibrium 

  6. An Example for Bayesian Nash Equilibrium: Public Good Provision 

  7. An Example for Bayesian Nash Equilibrium: Lemons Problem 

  8. An Example for Bayesian Nash Equilibrium: First Price Auction 

 

TOPIC 10: AUCTION THEORY 

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  1. Auction Theory: The Introduction

  2. Independent Private Value Auctions: The Model

  3. Vickrey (Second Price) Auction: The Game

  4. Solving Vickrey (Second Price) Auction: Weakly Dominant Strategy Equilibrium

  5. Solving First Price Auction with N Bidders: Part 1

  6. Solving First Price Auction with N Bidders: Part 2

  7. Solving First Price Auction with N Bidders: Part 3

  8. Strategic and Revenue Equivalence between First, Second and English Auctions

  9. Calculating Expected Revenue in Vickrey (Second Price) Auction

  10. Calculating Expected Revenue in First Price Auction

  11. Revenue Equivalence Theorem

  12. Common Value Auctions and Winner's Curse

  13. Auction Design

 

TOPIC 11: MECHANISM DESIGN 

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  1. What is Mechanism Design?

  2. Mechanism Design Example: Cake Division Problem, Divide and Choose Rule

  3. Mechanism Design Example: Public Good Project

  4. Mechanism Design Theory: The General Setting

  5. Social Choice Functions

  6. Mechanisms

  7. Dominant Strategy Mechanism Design

  8. Direct Mechanisms, Dominant Strategy Incentive Compatibility, and Revelation Principle

  9. Gibbard - Satterthwaite Impossibility Theorem Revisited

  10. Single Peaked Preferences

  11. Strategy Proof Mechanisms over Single Peaked Preferences: The Median Voting Rule

  12. Vickrey–Clarke–Groves (VCG) Mechanism (a.k.a Pivotal Mechanism)

  13. VCG Mechanism and Vickrey Auction

  14. Budget Balancedness and Individual Rationality of VCG Mechanism

  15. An Application of VCG Mechanism: Bilateral Trade

  16. Bilateral Trade: Calculating VCG Mechanism

  17. Bilateral Trade: VCG Mechanism Fails Budget Balancedness and Individual Rationality

  18. Bilateral Trade: Proving Strategy-Proofness of VCG Mechanism

  19. Bayesian Mechanism Design

  20. Bayesian Mechanism Design: Ex-post, Interim, and Ex-ante Individual rationality

 

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