Algorithmic Game Theory

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:

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