|English: mathematical game theory (Applied mathematics). עברית: tank_problem_n_players (Photo credit: Wikipedia)|
As an effort to share guidance for dynamic, 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 differentagents’ 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.
problem sets. We recommend that you complete the problem set for each
week within that week, although the hard deadline is two weeks from the
release date. On the fifth week, we will have a final exam.
Week 1. Social Choice
Week 2. Mechanism Design
Week 3. Efficient Mechanisms
Week 4. Auctions
Week 5-6. Final exam and final problem set.
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).
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations,
by Yoav Shoham and Kevin Leyton-Brown; Cambridge University Press,
2009. This book has the same structure as the course, and covers most of
the same material. It is available as a free PDF download from the link
above or for sale as a physical book from (e.g.) amazon.com.
A Brief Introduction to the Basics of Game Theory,
by Matthew O. Jackson. These notes offer a quick introduction to the
basics of game theory; they are available as a free PDF download.