Non-cooperative game theory is a branch of game theory for the resolution of
conflicts among players (agents), each behaving selfishly to optimize one’s own well-
being subject to resource limitations and potentially other restrictions coming from
rival’s actions. While being a standard modelling technique in economics, the Nash paradigm recently received further attention in connection with adversarial machine learning and multi-agent reinforcment learning, as well as challenging problems in distributed optimal control. The quest for efficient numerical algorithms and the analysis of their complexity thus became an important question in the modern theory of computational game theory. In this course we will introduce the basic tools of these modern techniques. 

Dates    Topic     Time
9.12.2026 Introduction to Normal form games 9:00-12:00
10.12.2026 LP Formulation for Zero-Sum games 10:00-12:00
16.12.2026 Elements of Mathematical Programming 10:00-12:00
17.12.2026 Potential and congestion games. 10:00-12:00
18.12.2026 Finite-Dimensional Variational Inequalities 10:00-12:00
21.12.2027 Online learning and regret minimization in games. 10:00-12:00
11.01.2027 Online learning and regret minimization in games. 10:00-12:00
13.01.2027 Learning dynamics and equilibrium selection 10:00-12:00
19.01.2027 Markov decision processes 10:00-12:00
20.01.2027 Stochastic games and multi-agent reinforcement learning 10:00-12:00
25.01.2027 Stochastic games and multi-agent reinforcement learning 9:00-12:00

After completing this course, students will know how to model multi-agent and strategic optimization problems in large-scale settings. They will be aware of computational approaches to Nash equilibrium, as well as learning approaches. Modern applications, like multi-agent reinforcement learning will be discussed as well.

Attendance is mandatory (80 % of the classes).

The course is a combination of lectures and tutorial style classes.

In order to successfully pass the course, the following assessement criteria need to be satisfied:

•  Handing in take home assignments (20 points)
• Presentation (20  points) 
• Oral exam (60 points) 

In total students can reach 100 points.

The grading of the course follows the scheme below:

Genügend (4) ≥ 50 , Befriedigend (3) ≥ 60, Gut (2) ≥ 70, Sehr gut (1) ≥ 80.

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Recommended Literature:

• Maschler, Michael, Shmuel Zamir, and Eilon Solan. Game theory. Cambridge University Press, 2020.
• A Modern Introduction to Online Learning by Francesco Orabona
• Facchinei, F., Kanzow, C. (2010). Generalized Nash equilibrium problems. Annals of Operations Research, 175(1), 177-211.
• Cesa-Bianchi, N., Lugosi, G. (2006). Prediction, learning, and games (Vol. 1, No. 1.1). Cambridge: Cambridge university press.
• Albrecht, S. V., Christianos, F., Schäfer, L. (2024). Multi-agent reinforcement learning: Foundations and modern approaches. MIT Press.