Recommended Course Outline 

This is a course outline that I use for my graduate-level game theory classes. It includes an ordered list of topics and lecture videos. It's important to watch the videos in the proper order because each concept builds on the ones introduced in previous videos. This will help ensure effective learning.

Course Description and Objective

This is a course designed for graduate students which offers an introduction to game theory and strategic thinking. It mainly focuses on the theory of cooperative and non-cooperative games with an emphasis on economic applications. Game theory deals with multi-person decision problems where the actions of each decision maker or player may have an impact on the payoffs of others. In such situations, making optimal decisions requires strategic thinking. One must consider how their actions can influence the incentives of other players, and whether those players 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

1. "Game Theory” by Drew Fudenberg and Jean Tirole.

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

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

4. “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