CS639: Introduction to Algorithmic Game Theory & Mechanism Design

Overview

Game theory is a mathematical framework to study interactions between multiple strategic agents, where agents view these interactions as “games” they are trying to “win”. Mechanism design studies the design of such interactions so as to obtain socially desirable outcomes. In this class, we will delve into both these topics through the lens of a computer scientist. We will examine questions such as: How does strategic behavior from a self-interested agent affect the other agents and society at large? Under what conditions do such interactions have equilibria (stable outcomes)? How can we learn/approximate such equilibria? How should we account for strategic behavior when designing social systems so as to achieve socially desirable equilibria? When multiple agents can cooperate to achieve more than the sum of their parts, how do we divide the value created among the agents? To study these questions, we will use tools from several areas such as probability, calculus, optimization, algorithms, and online machine learning.

This class is primarily targeted towards advanced undergraduate and early graduate students with a strong background in mathematics and algorithms.

Course staff

Instructor: Kirthevasan Kandasamy.
E-mail: kandasamy@cs{dot}wisc{dot}edu.
Office hours: Tuesday and Thursday. 5:15 PM - 6:00 PM at ENGR HALL 3355 (immediately after class).

Teaching assistant: Joon Suk Huh.
E-mail: jhuh23@wisc{dot}edu.
Office hours: Wednesday 2:30 - 4:00 pm at CS5388.

Grader: Ankur Sonawane.
E-mail: ankur.sonawane@wisc{dot}edu.

Lectures

Tuesday, and Thursday. 4:00 PM – 5:15 PM. ENGR HALL 3355.
Lectures will primarily be on the whiteboard. While we will not provide lecture notes, we will usually point to relevant reading material. However, students are strongly encouraged to attend class.

Topics

This is a tentative list of topics that we intend to cover in this class. The course staff reserves the right to modify the syllabus as they see fit.

• Game theory fundamentals

  • General-sum games, Nash equilibrium

  • Zero-sum games, minimax theorem

  • Potential games, best response dynamics

  • Price of anarchy/stability

  • Other equilibrium concepts

• Mechanism design

  • Stable matching

  • Trading agents

  • Fair resource allocation

  • VCG Mechanism

  • Revenue maximization in single-parameter auctions

• Cooperative game theory

  • Axiomatic bargaining

  • Coalitional games, the core, Shapley value

• Game theory and machine learning

  • Online learning and the experts problem

  • Learning in games, minimax theorem, swap regret

  • Online learning and bandits for mechanism design

Prerequisites

CS240, CS475, Econ301, or Econ 311.
I may waive this requirement, but it is the student's responsibility to have an adequate background in probability, linear algebra, calculus, and algorithms. I will not be doing a review of these topics at the beginning of the class. Students are also expected to be comfortable with mathematical proofs and logical reasoning.

I will release a set of diagnostic questions as Homework 0 at the beginning of class. While you are not expected to know the solutions right away, you should be able to solve most of the questions with reasonable effort after looking up any necessary references.

Recommended resources

The recommended textbook for the class is Game Theory, Alive by Anna Karlin and Yuval Peres. A pdf version of the book is free to download.
In addition, the following resources are excellent references for this class.

• Algorithmic Game Theory, Noam Nisan, Tim Roughgarden, Eva Tardos, Vijay V. Vazirani.

• Tim Roughgarden's lecture notes, Incentives in Computer Science, Algorithmic Game Theory.

• Amy Greenwald's lecture notes, Topics In Algorithmic Game Theory.

Logistics

Canvas: We will use canvas for homeworks.

Piazza: Please sign up for the class on piazza via this link. See the Canvas announcement for the access code.

• Piazza will be used for most announcements. But please check Canvas for announcements as well.

• If you have any questions about class, we strongly recommend contacting the course staff via Piazza instead of email. Please post your question publicly if you feel that other students may be able to answer it, or if you think that other students may benefit from the answer. We will prioritize public questions when answering them.

• You may use Piazza for peer discussions about lectures or clarifications about homework questions.

Grading

Your grade will be determined by homeworks, a mid-term and a final exam. See the grading page for more details.