Fall 2018

Professor: Aaron Roth

TAs: Adel Boyarsky, William Brown, Christopher Jung (Head TA), Arnab Sarkar, Aditya Srivatsan

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

Room: Town 337

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. A recommended textbook is Twenty Lectures on Algorithmic Game Theory. Another useful reference is Algorithmic Game Theory, for which you should be able to also find a PDF on the web.

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/fall2018/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: Adel Boyarsky, William Brown, Christopher Jung (Head TA), Arnab Sarkar, Aditya Srivatsan

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

Room: Town 337

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. A recommended textbook is Twenty Lectures on Algorithmic Game Theory. Another useful reference is Algorithmic Game Theory, for which you should be able to also find a PDF on the web.

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/fall2018/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: 9NX2E5.

- Problem Set 1. Due Thursday, September 13 before the start of class.
- Problem Set 2. Due Tuesday, October 2 before the start of class.
- Problem Set 3. Due Tuesday, October 16 before the start of class.
- MIDTERM. Tuesday, October 23. In class.
- Problem Set 4. Due Tuesday, November 6 before the start of class.
- Problem Set 5. Due Tuesday, November 20 before the start of class.
- Problem Set 6. Due Tuesday, December 4 before the start of class.

Lectures:

- Lecture 1: Overview.
- Lecture 2: Basic Definitions.
- Lecture 3: Congestion Games and Best Response Dynamics.
- Lecture 4: Characterizing Best Response Dynamics Convergence.
- Lecture 5: Learning from Expert Advice --- the Halving Algorithm.
- Lecture 6: Learning from Expert Advice --- the Polynomial Weights Algorithm.
- Lecture 7: Zero Sum Games.
- Lecture 8: Proof of the Min-Max Theorem.
- Lecture 9: Convergence of No Regret Dynamics in Seperable n-player Zero Sum Games.
- Lecture 10: Correlated Equilibrium.
- Lecture 11: Learning Algorithms Converging to Correlated Equilibrium.
- Lecture 12: Price of Anarchy and Stability.
- Lecture 13: Pareto Optimal Exchange: The Top Trading Cycles Algorithm.
- Lecture 14: Stable Matchings: The Deferred Acceptance Algorithm.
- Lecture 15: Walrasian Equilibrium: Simultanious Ascending Price Auctions.
- Lecture 16: Auction Design: The VCG Mechanism.
- Lecture 17: Auction Design in Single Parameter Domains.
- Lecture 18: Special Lecture --- VOTING and social choice. (Notes borrowed from Bo Waggoner)
- Lecture 19: Start Knapsack Auctions.
- Lecture 20: Finish Knapsack Auctions.
- Lecture 21: Profit Maximization and Random Sampling Auctions.
- Lecture 22: Online Auctions via Polynomial Weights.
- Lecture 23: Bandit Algorithms and Dynamic Pricing.