Game Theory II: Advanced Applications
by Matthew O. Jackson, Kevin Leyton-Brown, Yoav Shoham
Popularized by movies such as "A Beautiful Mind", game theory is the mathematical modeling of strategic interaction among rational (and irrational) agents. Over four weeks of lectures, this advanced course considers how to design interactions between agents in order to achieve good social outcomes. Three main topics are covered: social choice theory (i.e., collective decision making), mechanism design, and auctions.
In the first week we consider the problem of aggregating different agents' preferences, discussing voting rules and the challenges faced in collective decision making. We present some of the most important theoretical results in the area: notably, Arrow's Theorem, which proves that there is no "perfect" voting system, and also the Gibbard-Satterthwaite and Muller-Satterthwaite Theorems. We move on to consider the problem of making collective decisions when agents are self interested and can strategically misreport their preferences. We explain "mechanism design" -- a broad framework for designing interactions between self-interested agents -- and give some key theoretical results. Our third week focuses on the problem of designing mechanisms to maximize aggregate happiness across agents, and presents the powerful family of Vickrey-Clarke-Groves mechanisms. The course wraps up with a fourth week that considers the problem of allocating scarce resources among self-interested agents, and that provides an introduction to auction theory.
You must be comfortable with mathematical thinking and rigorous arguments. Relatively little specific math is required; the course involves lightweight probability theory (for example, you should know what a conditional probability is) and very lightweight calculus (for instance, taking a derivative).
The course consists of the following materials:
- Videos. The lectures are delivered via videos, which are broken into small chunks, usually between five and fifteen minutes each. There will be about an hour and a half of video content per week. You may watch the lecture videos at your convenience.
Lower-resolution videos are also available for those with slow internet connections.
You can also find the videos on : our youtube channel
- Slides. We have made available pdf files of all the lecture slides.
- Ungraded Practice Quizzes. There will be non-graded short "quiz" questions that will follow some of the videos to help you gauge your understanding.
- Online Lab Exercises. After some of the videos, we will ask you to go online to a specific url (that will be provided to you at that point) to play some games. These are entirely optional, and designed to illustrate some of the concepts from
- Graded Problem Sets. There will also be graded weekly problem sets that you will also answer online, but may work through offline. You may discuss problems from the problem sets with other students in an online forum, without providing explicit answers.
- Final Exam. There will be an online final exam.
The following background readings provide more detailed coverage of the course material:
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, by Yoav Shoham and Kevin Leyton-Brown; Cambridge University Press, 2009. This book covers most of the material. It is available as a PDF download from the link above or for sale as a physical book from (e.g.) amazon.com.
Mechanism Theory, by Matthew O. Jackson. These notes provide the basics of social choice and mechanism design - covering weeks 2, 3, and part of 4; they are available as a free PDF download
Matching, Auctions, and Market Design, by Matthew O. Jackson. These notes cover the basics of auctions and market design - covering week 4; they are available as a free PDF download
A Brief Introduction to the Basics of Game Theory, by
Matthew O. Jackson. These notes provide an introduction to the basics of game theory; they are available as a free PDF download
A Crash Course in Implementation Theory, by
Matthew O. Jackson. This goes beyond the course to further advanced topics in mechanism design (implementation theory). (If you cannot access the link above, you can
download the paper directly for your own educational use only here: A Crash Course in Implementation Theory)
Your grade in the course will be based solely on the problem sets (70 percent of your grade) and the final exam (30 percent of your grade).
You are free to follow the course without completing the problem sets or final, but then will not receive a certificate of completion.
If you have any questions, please do not contact the professors directly, as with over one hundred thousand of students it is infeasible for us to respond. The course includes on-line Q&A forums where students can post and respond
to questions. This will go live in parallel with the first lectures. Students rank questions and answers, so that the most important questions and the best answers bubble to the top. TAs and the professors will periodically monitor these forums, so
that important questions not answered by other students will be addressed.
Week 1: Social Choice
Week 2: Mechanism Design
Week 3: Efficient Mechanisms
Week 4: Auctions
Week 5: Final Exam Available