Spring 2020

Professor: Aaron Roth

TAs: Joseph Goodman, Jialin Wang, William Wang

Title: Tuesday/Thursday 3:00-4:30

Room: DRLB A8

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 (20%), and a final exam (30%).

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 Piazza to discuss class material, answer questions, and make announcements. The Piazza page for NETS 412 is piazza.com/upenn/spring2020/nets412. Students are encouraged to ask questions about the material on Piazza so that everyone can benefit and contribute to their answers.

Topics Covered:

TAs: Joseph Goodman, Jialin Wang, William Wang

Title: Tuesday/Thursday 3:00-4:30

Room: DRLB A8

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 (20%), and a final exam (30%).

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 Piazza to discuss class material, answer questions, and make announcements. The Piazza page for NETS 412 is piazza.com/upenn/spring2020/nets412. Students are encouraged to ask questions about the material on Piazza 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: MNEBEJ.

- Problem Set 1. Due by the start of class, Tuesday February 4, 2020.
- Problem Set 2. Due by the start of class, Tuesday February 18, 2020.
- Problem Set 3. Due by the start of class, Tuesday March 3, 2020.
- Problem Set 4. Due by the start of class, Tuesday March 24, 2020.
- Problem Set 5. Due by the start of class, Tuesday April 7, 2020.
- Problem Set 6. Due by the start of class, Tuesday April 28, 2020.

All post-pandemic lectures will take place on Zoom at the usual time (Tuesday/Thursday at 3:00PM Eastern Time) here: https://zoom.us/j/226580494.

Lectures:

- Lecture 1. Basic definitions, iterated elimination of dominated strategies. January 16, 2020.
- Course Overview. Watch this video lecture the week of 1/21, enter your guess for the "Guess 2/3 the Average" game (must be logged into your SEAS Google account), and discuss the Islanders problem on Piazza.
- Lecture 3. Congestion games and best response dynamics. January 28, 2020.
- Lecture 4. Characterizing when best response dynamics works. January 30, 2020.
- Lecture 5. Begin no regret learning. The halving algorithm and the weighted majority algorithm. February 4, 2020.
- Lecture 6. Finish no regret learning. The polynomial weights algorithm. February 6, 2020.
- Lecture 7. Zero Sum Games and the Minmax theorem. February 11, 2020.
- Lecture 8. Convergence of the PW algorithm to equilibrium in seperable multi-player zero sum games. February 13, 2020.
- Lecture 9. Correlated and Coarse Correlated Equilibria. February 18, 2020.
- Lecture 10. Swap Regret and Computing Correlated Equilibria. February 20, 2020.
- Lecture 11. The Price of Anarchy and Stability. February 25, 2020.
- Lecture 12. Begin mechanism design! Exchange Markets and Top Trading Cycles. February 27, 2020.
- Lecture 13. Stable Matchings March 3, 2020.
- Lecture 14. Walrasian Equilibrium and Market Dynamics. March 5, 2020.
- University closed due to global pandemic. March 17, 19, 2020.
- Lecture 15. Special Topic: The SIR Epidemic Model. March 24, 2020. Video here. Adapted from Easley/Kleinberg Chapter 21.
- Lecture 16. The VCG Mechanism. March 26, 2020. Video here.
- Lecture 17. Characterizing Truthfulness in Single Parameter Domains. March 31, 2020. Video here.
- Lecture 18. Knapsack Auctions. April 2, 2020. Video here.
- Lecture 19. Maximizing Revenue. April 7, 2020. Video here.
- Lecture 20. Approximating Optimal Revenue and Welfare with Posted Prices via the Prophet Inequality. April 9, 2020. Video here.
- Lecture 21. Prior-Free Mechanism Design: Maximizing Revenue Instance by Instance with the Random Sampling Auction. April 14, 2020. Video here.
- Lecture 22. Prior-Free Me chanism Design: Maximizing Revenue Online using the Polynomial Weights Algorithm April 16, 2020. Video here.
- Lecture 23. Dynamic Pricing via Bandit Algorithms. April 21, 2020. Video here.
- Lecture 24. Mechanism Design via Differential Privacy. April 23, 2020. Video here.
- Lecture 25. Game Theoretic Aspects of Algorithmic Fairness. April 28, 2020. Video here.