
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.
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,
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understand solution concepts in cooperative and non-cooperative games (whether it is in strategic or extensive form), and
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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
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Dominant and dominated strategy, dominant strategy equilibrium
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Solving Second Price Auction with Complete Information: An Equilibrium
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Solving Second Price Auction with Complete Information: All Equilibrium
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Solving Nash Demand Game with Outside Option: All Equilibrium
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Proof of Nash Theorem
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Never Best Response, IESDS, and IEWDS
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Rationalizability
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Correlated Equilibrium
TOPIC 2: BASICS OF NON-COOPERATIVE GAME THEORY: EXTENSIVE FORM GAMES WITH COMPLETE INFORMATION
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Describing extensive form games: Part 2 (Player functions and information sets)
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Games with Perfect Recall : Equivalence of Mixed and Behavioral Strategies
TOPIC 3: SOLVING EXTENSIVE FORM GAMES - APPLICATIONS
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How to find Subgame Perfect Nash equilibrium of Simple Games: Backward Induction
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How to find Subgame Perfect Nash equilibrium of Simple Games with Imperfect Information
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Rubinstein' Alternating Offer Bargaining Game and its Solution for the Two-Period Version
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Rubinstein's Alternating Offer Bargaining Game and its Solution for the Infinite Horizon Version
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Finding Subgame Perfect Nash Equilibrium of a Finite Horizon Repeated Game: An Example
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Infinitely Repeated Bertrand Competition: Collusion and Monopoly Pricing
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Finding Nash Equilibrium of an Extensive Game with Imperfect Information: An Example
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Robustness of Equilibrium Under Affine Payoff Transformations
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Why is One-Shot Deviation Property Correct and the Key for Calculating SPNE
TOPIC 4: INTRODUCTION TO COOPERATIVE GAME THEORY AND ITS SOLUTION CONCEPTS
TOPIC 5: COOPERATIVE (NASH) BARGAINING
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Pareto, Weak Pareto, and Individually Rational Sets of Bargaining Problems
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Cooperative Bargaining Axioms: Pareto Optimality and Symmetry
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Cooperative Bargaining Axioms: Independence of Irrelevant Alternatives (IIA)
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Independence of Irrelevant Alternatives (IIA) and Nash Bargaining Rule
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Solving for Kalai Smorodinsky Bargaining Outcome: Two Examples
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Bargaining Axioms: Translation Invariance and Strong Monotonicity
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Calculating Egalitarian Rule Bargaining Solution: A numerical Example
TOPIC 6: BANKRUPTCY (CLAIMS) PROBLEM
TOPIC 7: MATCHING THEORY
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A Simple Theory of Matching: Gale and Shapley's One-to-One Matching
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Strategy-Proof and Stable Mechanisms for One-to-One Matching
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You Ask (Request) My House - I get Your Turn (YRMH-IGYT) Algorithm: A Numerical Example
TOPIC 8: VOTING
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Voting Axioms: Independence of Irrelevant Alternatives (IIA)
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Arrow's Impossibility Theorem and Condorcet Paradox (Cycles)
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Strategic Voting: Gibbard-Satterthwaite Impossibility Theorem
TOPIC 9: BAYESIAN GAMES AND BAYESIAN NASH EQUILIBRIUM
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An Example for Bayesian Nash Equilibrium: Public Good Provision
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An Example for Bayesian Nash Equilibrium: First Price Auction
TOPIC 10: AUCTION THEORY
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Solving Vickrey (Second Price) Auction: Weakly Dominant Strategy Equilibrium
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Strategic and Revenue Equivalence between First, Second and English Auctions
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Calculating Expected Revenue in Vickrey (Second Price) Auction
TOPIC 11: MECHANISM DESIGN
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Mechanism Design Example: Cake Division Problem, Divide and Choose Rule
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Direct Mechanisms, Dominant Strategy Incentive Compatibility, and Revelation Principle
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Strategy Proof Mechanisms over Single Peaked Preferences: The Median Voting Rule
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Vickrey–Clarke–Groves (VCG) Mechanism (a.k.a Pivotal Mechanism)
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Budget Balancedness and Individual Rationality of VCG Mechanism
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Bilateral Trade: VCG Mechanism Fails Budget Balancedness and Individual Rationality
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Bilateral Trade: Proving Strategy-Proofness of VCG Mechanism
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Bayesian Mechanism Design: Ex-post, Interim, and Ex-ante Individual rationality