Spring 2024

Professor: Aaron Roth

TAs: Mirah Shi, Kevin Zhou, Jack Hourigan, Insha Lakhani, Michael O'Farrell, Arunim Agarwal

Title: Tuesday/Thursday 3:30-4:59pm

Room: FAGN 216

Overview: In this course, we will take an algorithmic perspective on problems in game theory. We will consider questions such as: how should an auction for scarce goods be structured if the seller wishes to maximize his revenue? How badly will traffic be snarled if drivers each selfishly try to minimize their commute time, compared to if a benevolent dictator directed traffic? How can couples be paired so that no two couples wish to swap partners in hindsight? How can we find kidney-exchange cycles to incentivize people to participate in the exchange, without using money? How can we incentivize weather men not to lie to us about*WIND* and *RAIN*?
How can we set prices so that all goods get sold, and everyone gets their favorite good?

Prerequisites: This will be a mathematically rigorous theory course for advanced undergraduates. Students should have taken, or be taking concurrently a course in algorithms (such as CIS 320), be mathematically mature, and be familiar with big-O notation. Prior coursework in game theory is helpful, but not necessary. Everything will be presented from first principles.

Goals and Grading: The goal of this course is to give students a rigorous introduction to game theory from a computer science perspective, and to prepare students to think about economic and algorithmic interactions from the perspective of incentives. Grading will be based on participation (5%), problem sets (45%), a midterm (25%), and a final exam (25%).

Textbook: There is no required textbook. Several recommended books are Twenty Lectures on Algorithmic Game Theory, Algorithmic Game Theory, and The Ethical Algorithm (Chapter 3).

Office Hours and Discussion: Office Hours: See Piazza

We will be using Slack to discuss class material, answer questions, and make announcements. Registered students should have received an invite to the slack workspace; if you should have one and don't, email the professor. Students are encouraged to ask questions about the material on Slack so that everyone can benefit and contribute to their answers.

Topics Covered:

TAs: Mirah Shi, Kevin Zhou, Jack Hourigan, Insha Lakhani, Michael O'Farrell, Arunim Agarwal

Title: Tuesday/Thursday 3:30-4:59pm

Room: FAGN 216

Overview: In this course, we will take an algorithmic perspective on problems in game theory. We will consider questions such as: how should an auction for scarce goods be structured if the seller wishes to maximize his revenue? How badly will traffic be snarled if drivers each selfishly try to minimize their commute time, compared to if a benevolent dictator directed traffic? How can couples be paired so that no two couples wish to swap partners in hindsight? How can we find kidney-exchange cycles to incentivize people to participate in the exchange, without using money? How can we incentivize weather men not to lie to us about

Prerequisites: This will be a mathematically rigorous theory course for advanced undergraduates. Students should have taken, or be taking concurrently a course in algorithms (such as CIS 320), be mathematically mature, and be familiar with big-O notation. Prior coursework in game theory is helpful, but not necessary. Everything will be presented from first principles.

Goals and Grading: The goal of this course is to give students a rigorous introduction to game theory from a computer science perspective, and to prepare students to think about economic and algorithmic interactions from the perspective of incentives. Grading will be based on participation (5%), problem sets (45%), a midterm (25%), and a final exam (25%).

Textbook: There is no required textbook. Several recommended books are Twenty Lectures on Algorithmic Game Theory, Algorithmic Game Theory, and The Ethical Algorithm (Chapter 3).

Office Hours and Discussion: Office Hours: See Piazza

We will be using Slack to discuss class material, answer questions, and make announcements. Registered students should have received an invite to the slack workspace; if you should have one and don't, email the professor. Students are encouraged to ask questions about the material on Slack so that everyone can benefit and contribute to their answers.

Topics Covered:

- Part 1: Game Theory and Game Dynamics
- Quick introduction to game theory: Zero sum and general sum games, Minmax strategies, Nash equilibrium, correlated equilibrium.
- Game Dynamics: Weighted Majority Algorithm
- Game Dynamics: Bandit Algorithms
- Game Dynamics: converging to Nash equilibrium in zero sum games; Game dynamics converging to correlated equilibrium in general sum games
- Game Dynamics: Best Response Dynamics and Potential Games.
- Price of anarchy and price of stability: Definition, routing games, hoteling games
- More if time allows...
- Part 2: Assignment Problems and Mechanism Design
- Stable Matchings and the Deferred Acceptance Algorithm
- Market Equilibrium and Gross Substitute Preferences
- Auction basics: First price auctions, second price auctions, truthfulness
- Maximizing welfare: The VCG Mechanism
- Auctions and Approximation Algorithms
- Combinatorial Auctions
- Online Auctions
- Maximizing revenue: Prior Free Mechanism Design
- Online auctions for digital goods
- Proper Scoring Rules and Prediction Markets
- More if time allows...

Problem sets will be turned in and graded via GradeScope. The course entry code is: VB77XX.

- Problem Set 1. Due February 6 Before Class
- Problem Set 2. Due February 20 Before Class
- Problem Set 3. Due March 12 Before Class
- Problem Set 4. Due March 26 Before Class
- Problem Set 5. Due April 9 Before Class
- Problem Set 6. Due April 23 Before Class

Lectures:

- Lecture 1: Course Overview and Basics.
- Lecture 2: Basic Definitions
- Lecture 3: Congestion Games and Best Response Dynamics
- Lecture 4: Characterizing convergence of best respnse dynamics
- Lecture 5: Begin Polynomial Weights (Analyzing the Halving Algorithm)
- Lecture 6: Finish Polynomial Weights
- Lecture 7: Zero Sum Games and the Minimax Theorem
- Lecture 8: No Regret Learning Converges to Equilibria in Separable Zero Sum Games
- Lecture 9: Correlated Equilibrium
- Lecture 10: Guaranteeing no "Swap Regret" and Convergence to Correlated Equilibrium
- Lecture 11: The Price of Anarchy and Stability
- Lecture 12: Pareto Optimal Exchange and Top Trading Cycles
- Lecture 13: Stable Matchings and Deferred Acceptance
- Lecture 14: Walrasian Equilibrium
- Lecture 15: Begin Auction Design: The VCG Mechanism
- Lecture 16: Auctions in Single Parameter Domains
- Lecture 17: Approximation in Mechanism Design: Knapsack Auctions
- Lecture 18: Revenue Optimal Auctions
- Lecture 19: Posted Prices, Profits, and Prophets
- Lecture 20: Prior Free Revenue Maximization: Random Sampling Auctions
- Lecture 21: Sequential Auctions via Polynomial Weights
- Lecture 22: Dynamic Pricing and Learning from "Bandit" Feedback
- Lecture 23: Truthful Belief Elicitation and Proper Scoring Rules
- Lecture 24: Game Theory for ML: Calibrated Forecasting
- Lecture 25: Game Theory for ML 2: Boosting