CS639: Algorithmic Game Theory & Learning

Overview

Have you ever wondered how Google runs large-scale ad auctions in milliseconds, how ride-sharing platforms like Uber balance supply and demand, how organizations fairly allocate shared compute resources, how the national resident matching program pairs medical students with hospitals according to each others’ preferences, or how kidney exchange networks form life-saving chains of compatible donors and recipients? Behind all of these systems lies game theory-the mathematical study of how self-interested agents interact, compete, and cooperate. This course will teach you how to model such strategic interactions, how to compute equilibrium behavior in such interactions, and how to design algorithms and systems that lead to stable and socially desirable outcomes.

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? We will studey these questions, through the lens of computer science, using ideas from theoretical computer science, machine learning, optimization, probability, and calculus.

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: Tuesdays 2:00 PM - 3:30 PM at MH5506.

Grader: David Zikel.
E-mail: zikel@wisc{dot}edu.

Lectures

Tuesday and Thursday. 11:00 AM – 12:15 PM. PSYCHOLOGY 103.

Lectures will be based on prepared slides, with selected portions of the material—particularly mathematically intensive components—written live during class on a tablet and projected onto the screen. A complete set of slides will be made available to students in advance. However, the slides are intended as teaching aids only and do not include all material discussed in lecture. Students are strongly encouraged to attend lectures and take their own notes.

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.

• General sum games

  • Normal form games, Dominant strategy and Nash equilibria, Safe strategies

  • Indifference principle

  • Potential games, best response dynamics

  • Price of anarchy/stability

  • Correlated and coarse correlated equilibria

• Zero sum games

  • Minimax theorem

  • Case study: Generative adversarial networks

• Solving games via linear programming

  • Review of linear programs (LP)

  • Computing safe strategies via LPs

  • Computing correlated and coarse correlated equilibria via LPs

• Online learning

  • Experts problem and the Hedge algorithm

  • Adversarial bandits and the EXP3 algorithm

• Learning in games

  • Proof of the minimax theorem

  • Approximating Nash equilibria in zero sum games

  • Approximating coarse correlated equilibria

  • Correlated equilibria and swap regret

• Mechanism design without money

  • Trading agents, Kidney exchange

  • Stable matching

  • Fair resource allocation

• Mechanism design with money

  • VCG Mechanism

  • Revenue maximization in single-parameter auctions

  • Prophet inequalities

• Cooperative game theory

  • Axiomatic bargaining

  • Coalitional games, the core, Shapley value

  • Case study: collaboration in federated learning

• Truthful information elicitation (if time permits)

  • Scoring rules

  • Bayesian truth serum

  • Peer prediction

Prerequisites

(CS/MATH 240 or CS/MATH/STAT 475) and (MATH 320, 340, 341, 345 OR 375) Or Graduate/professional standing.
We may waive this requirement, but it is the student's responsibility to ensure that they have the necessary background. We will not review these topics at the beginning of the class.

A strong background in mathematics and algorithms is required. This is a demanding course intended for advanced undergraduate and early graduate students who enjoy rigorous proofs, abstraction, and algorithmic thinking. Students should also be comfortable writing simple programs to implement and test the concepts studied in the course.

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 proof-reading slides, a mid-term, final, and class participation. See the grading page for more details.