ECE752/493


Game-Theoretic Foundations of Multi-agent Systems

Winter 2026

Details


Time & location

Lectures: Tu, Th 13:00 - 14:20, E7 5353

Tutorials: Tu 20:00 - 20:50, E7 4433 (most likely online)

Teaching team
Prof. Seyed Majid Zahedi

Instructor

Prof. Seyed Majid Zahedi

Book appointments here

Eli Propp

GTA

Eli Propp

Description

This course is an introduction to the mathematical and computational foundations of modern multi-agent systems, with a focus on game theory, artificial intelligence, and machine learning. The course provides analytical tools to analyze and model multi-agent systems in which an agent's welfare is a function of not only their own actions, but also those of others. Tentative topics include normal-form games, extensive-form games, repeated games, stochastic games, Bayesian games, computation of solution concepts, and learning in multi-agent systems.

This course is part of the Engineering AI Option and the Computer Science AI Specialization.

Prereq
There are no formal prerequisites, and it is assumed that most students in the class will be unfamiliar with game theory, mechanism design, and multi-agent systems. Since some of the material is quite mathematically formal, students are expected to have introductory knowledge in probability theory (ECE203 or equivalents), computational complexity (ECE208 or equivalents), and algorithms (ECE250 or equivalents).
Antireq
Students will not be allowed to take this course if they have completed (or are currently taking) ECON412, CO456, CO759 (Algorithmic Game Theory), CS886 (Multi-agent Systems), and MSCI724 (Game Theory and Recent App)
Readings

Main textbook

Optional references

Evaluation

The course has two different grading schemes are as follows.

  • Undergraduate: 5% quizzes; 20% assignments; 25% (survey) project; 50% final exam
  • Graduate: 5% quizzes; 20% assignment; 45% (research) project; 30% final exam

Quizzes, assignments, and the final exam are the same for both schemes but have different percentage breakdowns in each scheme. The project, however, has different requirements in each scheme (see Policies for more details). Undergraduate students have the option of choosing the graduate grading scheme when they submit their project proposal.

Main Topics (tentative)

The course tentatively covers the following topics:

  • Introduction to multi-agent systems

    Overview of game theory and mechanism design, rationality and self-interest, utility theorem, risk attitudes

  • Normal-form games

    Pure and mixed-strategy Nash equilibrium, iterative elimination of dominated strategies, price of anarchy, correlated equilibrium, computing solution concepts of normal-form games

  • Extensive-form games

    Perfect and imperfect-information games, finite and infinite-horizon games, subgame-perfect equilibrium, backward induction, one-shot deviation principle

  • Beyond normal and extensive-form games

    Repeated games, stochastic games, Bayesian games, congestion games, trigger strategies, folk theorems, Bayes-Nash equilibrium, auctions, optimal auctions, revenue-equivalence theorem, incentive compatibility, VCG mechanisms

  • Learning in multi-agent systems

    Multi-agent reinforcement learning, fictitious play, Bayesian learning, regret-minimization learning

Announcements


Jan 4
Please sign up for the course on Piazza.

Schedule (tentative)


Week Day Lecture Reading Event
1 Tu 01/06

Introduction

Slides: PDF

Th 01/08

Preferences and utilities

Slides: PDF

MAS Ch3.1 and Appx A

Jan 7: makeup session

2 Tu 01/13

Games in normal form

Slides: PDF

MAS Ch3.2-3.4

Th 01/15
3 Tu 01/20
Th 01/22
4 Tu 01/27

Computing solution concepts of normal-form games

Slides: PDF

Codes: ZIP

MAS Ch4 and Appx B

Optional:

Th 01/29

Proposal deadline

5 Tu 02/03

Games in extended form

Slides: PDF

MAS Ch5

Th 02/05
6 Tu 02/10
Th 02/12

Repeated games

Slides: PDF

MAS Ch6.1

7 Tu 02/17 Reading week
Th 02/19
8 Tu 02/24 Midterm week
Th 02/26
9 Tu 03/03

Stochastic games

Slides: PDF

MAS Ch6.2

Th 03/05
10 Tu 03/10

Bayesian games

Slides: PDF

MAS Ch6.3-6.4 and Ch8.1-8.2

Th 03/12
11 Tu 03/17
Th 03/19

Learning in games

Slides: PDF

MAS Ch7

12 Tu 03/24
Th 03/26
13 Tu 03/31

Project presentations

Th 04/02

Apr 06: Project report deadline.

Assignments


Resources


Slides

GitHub repository

Sample exams

Waterloo ECEE752

Waterloo ECEE700

Policies


Assessments

Quiz policy

There will be an unspecified number of pop-up quizzes during the class.

Assignment policy

There will be between three and five assignments, each consisting of approximately three to five problems. Solutions will be graded based on both accuracy and presentation. Correct solutions that are poorly presented may not receive full marks.

Late submissions will be accepted with 15% penalty per day for only two days after the due date (the same policy is applied to project proposals and final reports).

Students can discuss the class material with other students. Students also can discuss with others about how to formulate assignment problems. However, students must write down their solutions by themselves. In particular, students may not take notes while they discuss assignments with others.

Any suspected plagiarism or infractions of this honor code will be reported to the appropriate Associate Dean.

Auditing

All students are welcome to audit the course unofficially without any requirements. However, for the audit to be officially recorded on their transcript, students must enroll in the course on Quest as an audit, attend the lectures, take the final exam, and achieve a minimum score of 30%.

Projects

Undergrad survey project

For the survey project, students will review a research paper in a subarea of multi-agent systems. There will be two milestones during the term: a proposal (10%) and a presentation (90%).

Proposal for undergrads

In the project proposal, students should form groups of no more than three and identify the paper they intend to review. They should also briefly describe the subarea of their chosen paper and explain the significance of the research. Students may consult this page for a list of suggested papers related to the course.

Undergraduate students can choose the graduate grading scheme when they submit their proposals. Those who decide to go with the graduate grading scheme have to follow the proposal format outlined below for grad students.

Final presentation for undergrads

In the final presentation, each group is expected to prepare slides for a 10-minute presentation, followed by a 10-minute question-and-answer period. The presentation should provide clear answers to the following questions:

  • What specific problem does this work address, and why is it important?
  • What was the state of the art in this area at the time of publication, and what limitations existed?
  • How does the paper advance the state of the art, and why is it more effective than prior approaches?
  • What are the key artifacts presented in the paper (e.g., methodology, hardware design, software algorithm, optimization or control technique)?
  • How were these artifacts implemented and evaluated?
  • What are the most important empirical or theoretical results?

All group members should be prepared to answer questions about the paper. The final grade will be the same for all members of a group and will depend on the quality and clarity of the presentation, as well as the answers provided by all group members during the question period.

Grad research project

For graduate students, an important part of this course is the research project. For the research project, students can work on the research project alone or in a team of at most three students; of course, teams are expected to work on more significant projects.

The goal of the research project is to try to do something novel, rather than merely a survey of existing work. Projects may be theoretical, experimental (based on simulations), experimental (based on real-world data), a useful software artifact, or any combination thereof. Creativity is encouraged. The only real constraint for the project is that it has to have something to do with the material covered in the course. Students are encouraged to talk to the course instructor if you are not sure about whether something is an appropriate project.

The final product is a writeup (in the form of a short research paper). Some projects may well lead to publishable papers (perhaps with some additional work). There will be 3 milestones during the course: proposal (10%), final presentation (50%), and final written report (40%).

Proposal for grads

In the project proposal, students should explain the topic of their project, what types of results they hope to obtain, and what some of the technical issues are that you will need to address. For graduate students, the course project could be related to their own ongoing research as long as it also has clear connections with the course material. If necessary, the course instructor can help with finding topics. Each proposal should include all the following.

  • Introduction: Introduce and motivate the project
  • Problem statement: Describe the purpose and the objective(s) of the project
  • Methodology: Describe methods and tools that will be deployed to tackle the problem
  • Related work: Overview the state-of-the-art by citing related research papers, ideally published recently in top-tier conferences or journals

Progress report for grads

Intermediate oral project progress report is optional. This report should explain what results each group has obtained already, what (if any) difficulties the group has encountered, and what the group plans to do to complete the project. Ideally, at this point, each group should already have some good results, so that it can spend the rest of the time on answering questions generated by the results, as well as preparing the writeup.

Final presentation and report for grads

Each group is expected to prepare slides for a 15-minute presentation, followed by a 10-minute question-and-answer period. The presentation should provide clear answers to the following questions:

  • What specific problem does your project address, and why is it important?
  • What was the state of the art in this area, and what limitations exist?
  • How does your project advance the state of the art, and why is it more effective than prior approaches?
  • What are the key artifacts of your project (e.g., methodology, hardware design, software algorithm, optimization or control technique)?
  • How are these artifacts implemented and evaluated?
  • What are your most important empirical or theoretical results?

All group members should be prepared to answer questions about the paper. The final grade will be the same for all members of a group and will depend on the quality and clarity of the presentation, as well as the answers provided by all group members during the question period.

Each group also has to prepare and submit a final project report by the end of the term using the ACM Master Article Template. For Microsoft Word, students should use the interim layout.docx, and for Latex they should use the sample-sigconf.tex file in the samples folder. Submitted reports with any other format/style will not be accepted.

Each report has to include (at least) the following sections: abstract, introduction, methodology, experimental results (if applicable), related work, conclusion, and references. Without references, each report should not be less than 5 and not more than 11 pages.

Other policies

Academic integrity policy

In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility. Check the Office of Academic Integrity for more information.

Grievance policy

A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70, Student Petitions and Grievances, Section 4. When in doubt, please be certain to contact the department's administrative assistant who will provide further assistance.

Discipline policy

A student is expected to know what constitutes academic integrity to avoid committing an academic offense, and to take responsibility for his/her actions. Check the Office of Academic Integrity for more information.

A student who is unsure whether an action constitutes an offense, or who needs help in learning how to avoid offenses (e.g., plagiarism, cheating) or about "rules" for group work/collaboration should seek guidance from the course instructor, academic advisor, or the undergraduate associate dean.

For information on categories of offenses and types of penalties, students should refer to Policy 71, Student Discipline. For typical penalties, check Guidelines for the Assessment of Penalties.

Appeals policy

A decision made or penalty imposed under Policy 70, Student Petitions and Grievances (other than a petition) or Policy 71, Student Discipline may be appealed if there is a ground. A student who believes he/she has a ground for an appeal should refer to Policy 72, Student Appeals.

Automatic system to detect plagiarism

Moss (Measure Of Software Similarity) will be used to screen each project in this course. Students' submissions are stored on a U.S. server, therefore students will be given an alternative if they are concerned about their privacy and/or security. Students will be given due notice about arrangements and alternatives for the use of Moss in this course.