February 23: Start of the course! We look forward to getting to know you.
Algorithmic Game Theory (AGT) is an interdisciplinary research area that lies in the intersection of Theoretical Computer Science, Discrete Mathematics and Economic Theory. The area builds upon game-theoretic foundations to study situations of strategic decision making, with a particular focus on computational and algorithmic aspects. It combines methodologies and techniques from several disciplines such as complexity theory, algorithm design, discrete and continuous optimization, online decision making and learning, auction and mechanism design, etc.
The overall goal of the course is to build up a mathematical toolbox of state-of-the-art models, methodologies and techniques to study the impact of strategic decision making and to develop efficient algorithms for such environments.
The main topics that will be covered in this course are:
selfish routing games and the price of anarchy
Braess paradox, Stackelberg routing, network tolls
best-response dynamics and potential games
complexity of equilibrium computation
quantifying the inefficiency of equilibria
equilibrium hierarchy and no-regret learning
smoothness and extension theorems
improving price of anarchy with predictions
prophet inequalities
fair division of indivisible goods
Besides the material covered in class, we will also ask you to study some material on your own and to solve three take-home assignments (see below).
We assume that the participants have a solid background knowledge of discrete optimization (in particular, fundamental algorithms, computational complexity, linear/convex programming, etc.) and probability theory; some basic knowledge of game theory is advantageous, but not a prerequisite for the course.
This course is part of the Dutch Network on the Mathematics of Operations Research (LNMB).
The course starts on February 23, 2026 (Lecture #1) and ends on May 4, 2026 (Lecture #9).
Date/Time:
Mondays, 11:00-12:45
Location:
Room HFG 611, Hans-Freudenthal Building
(Budapestlaan 6, 3584 CD Utrecht, see Google Maps)
All lectures will be given onsite in Utrecht.
Note:
There will be no lecture on April 6 (Easter) and April 27 (Kingsday).
We have a backup slot on May 11 which we might use if some lectures have to be cancelled.
The course will be given by Guido Schäfer and Pieter Kleer. Contact details are given below. Please feel free to approach us if you have any questions, comments or remarks related to the course.
Prof. Dr. Guido Schäfer
Networks and Optimization Group, Centrum Wiskunde & Informatica
Institute for Logic, Language and Computation, University of Amsterdam
Email: g.schaefer@cwi.nl
Dr. ir. Pieter Kleer
Department of Econometrics and Operations Research
Tilburg School of Economics and Management, Tilburg University
Email: p.s.kleer@tilburguniversity.edu
Assignments will be issued and have to be handed in as indicated below:
NOTE: tentative schedule
Assignment 1: issued March 2, due March 16
Assignment 2: issued March 30, due April 13
Assignment 3: issued May 4, due May 18
The assignments will be posted in the online material section below.
You are encouraged to work on the assignments in groups. The maximum group size is limited to two students. If you would like to be matched with a fellow student, please let us know.
IMPORTANT: (please read carefully!)
Collaboration is limited to your assigned group; working with other groups is not permitted.
If you use or consult external resources such as books, articles, websites, or AI/LLM tools (e.g., ChatGPT), you must clearly acknowledge these sources.
All submitted work must be written in your own words and reflect your own understanding. Copying solutions or relying on generated answers without comprehension is not permitted.
The use of AI tools is discouraged and should be limited to situations in which you are genuinely stuck and use them as a learning aid rather than as a solution generator. If you use AI tools, you must document this by including the relevant prompts (e.g., screenshots) together with a brief explanation of how the tool supported your reasoning.
You should be able to explain and justify every part of your submission upon request.
Solutions to the assignments must be submitted via the course upload folder before the stated deadline (due date, 23:59 CEST): upload folder
Submissions are expected to be typeset in LaTeX and provided as a compiled PDF; clear structure, consistent notation, and overall readability form part of the evaluation. Handwritten solutions are strongly discouraged and will only be accepted in exceptional cases. In such instances, the submission must be clearly legible, with sufficiently neat handwriting and high-quality scans (adequate contrast and resolution). Illegible submissions may receive no points.
The following books contain most of the material covered in class and are good references if you want to learn more.
[NRTV07]
N. Nisan, T. Roughgarden, E. Tardos, and V. V. Vazirani (Editors), Algorithmic Game Theory, Cambridge University Press, 2007.
Note: The full-text of the book (pdf) seems to be available online.
[Rou16]
T. Roughgarden, Twenty Lectures on Algorithmic Game Theory, Cambridge University Press, 2016.
Note: The full-text of the book (pdf) seems to be available online.
[SLB16]
Y. Shoham and K. Leyton-Brown, Multiagent Systems, Cambridge University Press, 2009.
Note: The full-text of the book (pdf) is available here.
[KP16]
A. R. Karlin and Y. Peres, Game Theory, Alive, American Mathematical Society, 2016.
Note: The full-text of the book (pdf) is available here.
The online material of the course can be found here (password will be provided in the lecture).