Algorithmic Game Theory

Spring 2012
Instructor: Aaron Roth
Time: Tuesday/Thursday 1:30-3:00 pm
Room: Towne 303

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 you be as successful at betting on horse races as the best horse racing expert, without knowing anything about horse racing?

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, problem sets, a midterm, and a final exam.

Textbook: A recommended textbook is Algorithmic Game Theory, which is also available for free on the web here (username=agt1user, password=camb2agt).

Office Hours and Discussion: By appointment in Levine 603.
We will be using Piazza to discuss class material and answer questions. The Piazza page for CIS 399 is Students are encouraged to ask questions about the material on Piazza 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, repeated games, Minmax strategies, Nash equilibrium, correlated equilibrium
    2. Game Dynamics: Sequential best response, weighted majority algorithm, fictitious play, perturbed follow the leader
    3. Game Dynamics converging to Nash equilibrium in zero sum games; Game dynamics converging to correlated equilibrium in general sum games
    4. Price of anarchy: Definition, routing games, hoteling games
    5. Smooth games and "Price of Total Anarchy"
    6. More if time allows...
  2. Part 2: Auctions and Mechanism Design
    1. Auction basics: First price auctions, second price auctions, truthfulness
    2. Maximizing welfare: The VCG Mechanism
    3. Ad Auctions on Google/Yahoo/Bing
    4. Maximizing revenue: Bayesian optimal auctions: How to set a reserve price
    5. Maximizing revenue: Prior Free Mechanism Design
    6. Online auctions for digital goods
    7. Stable Marriages and the Deferred Acceptance Algorithm
    8. More if time allows...

Problem Sets and Exams:
  1. Homework 1: Due Thursday, February 9 in class.
  2. Homework 2: Due Thursday, March 1 in class.
  3. Practice Midterm: Real Midterm will be February 23 in class.
  4. Homework 3: Due Tuesday, March 20 in class.
  5. Homework 4: Due Thursday, April 12 in class.
  6. Practice Final: Real Midterm will be April 24 in class.


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