Game Theory

2025/26/2

Second iteration of the Game Theory course for the AI Masters specialization, building on the first run. Two big changes this semester: a full set of practice notebooks now exists (NashPy from start to finish), and the grade is now driven entirely by the two midterms (no separate practice assignments this round). The lecture material has also been expanded with a final week on fairness, Pareto optimality, and social welfare.

Please note that the materials may contain small mistakes, typos, or even implementation bugs. I would appreciate any notifications about these issues sent to my email.

Lecture and Practice Content

Exams

The final grade is determined by the two midterms. Sample versions are released a week before the real thing so students know exactly what to expect.

Course Syllabus

Schedule

Lecture:

• Schedule: Wednesdays, 10:00 - 12:00
• Location: South Building, Room LD-2-502-01-11

Note:

• Hungarian: Déli Tömb LD-2-502-01-11

Practice:

• Schedule: Wednesdays, 12:00 - 14:00
• Location: South Building, Room 00-807

Note:

• Hungarian: Déli Tömb 00-807

Description

This course provides a rigorous introduction to Game Theory with a focus on its relevance for Artificial Intelligence and Multi-Agent Systems. Students will learn how to formally represent strategic interactions, analyze agent behavior, and evaluate solution concepts such as Nash equilibria, mixed strategies, and correlated equilibria.

The course progresses from foundational models of normal-form and extensive-form games to more advanced topics, including stochastic and repeated games, communication between agents, and evolutionary dynamics. Particular emphasis is placed on the computational aspects of game theory, such as the complexity of equilibrium computation, as well as on learning in games through methods like fictitious play, no-regret learning, and replicator dynamics.

Practical sessions complement the lectures by introducing computational tools, most notably NashPy, enabling students to model games, compute equilibria, and simulate adaptive dynamics. By the end of the semester, participants will have developed both the mathematical foundations and the computational skills required to analyze strategic interaction in AI contexts, bridging classical theory with modern applications in multi-agent reinforcement learning.

Grading

Your final grade is calculated using the formulas below:

Final Lecture Score (LS) = Midterm 1 (50 points) + Midterm 2 (50 points)
Final Score (FS) = LS

Prerequisites

• Python (moderate level)
• Linear Algebra and Probability (moderate level)
• Reinforcement Learning Concepts (advantageous but not required)

Tools and Frameworks

• Programming Language: Python
• Frameworks: PyTorch, NashPy
• Libraries: NumPy
• Additional Tools: Google Colab

Learning Objectives

• Understand the mathematical and conceptual foundations of Game Theory
• Learn classical solution concepts and their computational aspects
• Explore the role of Game Theory in AI and MARL
• Apply libraries like NashPy to model and analyze games
• Develop intuition for fairness, efficiency, and equilibrium concepts in strategic interaction

Recommended Reading

1. Bonanno, G. (2024). Game Theory (3rd ed.). University of California, Davis.
2. Axelrod, R. (1984). The Evolution of Cooperation. Basic Books.
3. Nisan, N., Roughgarden, T., Tardos, É., & Vazirani, V. V. (2007). Algorithmic Game Theory. Cambridge University Press.
4. Myerson, R. B. (1991). Game Theory: Analysis of Conflict. Harvard University Press.
5. Shoham, Y., & Leyton-Brown, K. (2008). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press.
6. Christianos, F. et al. (2023). Multi-Agent Reinforcement Learning: Foundations and Modern Approaches.
7. NashPy Documentation.