Game Theory
2025/26/1
This marks the first iteration of the new Game Theory course for the AI Masters specialization. Building a comprehensive Game Theory curriculum from scratch has been a significant challenge, and while this initial version is still a work in progress, it covers most of the essential topics in the field. With the focus heavily on developing lecture material, assignments, and exams, there hasn’t yet been an opportunity to create dedicated practice materials. My goal is to refine this into one of the strongest courses in our specialization.
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
Introduction to Game Theory.
NashPy: NFGs.
NashPy: Repeated Games.
NashPy: Computing Nash Equilibria.
NashPy: Mixed Strategies.
NashPy: Computing CE.
Assignment 1 deadline.
Fairness experiments.
Minimax implementations.
Minimax implementations part 2.
POSG examples.
NashPy: Bayesian Games.
Assignment 2 deadline.
Assignments
The two assignments correspond to the first and second halves of the course material, each covering practical implementations of the concepts introduced in lectures. They are designed to be completable using only the NashPy library and lecture content, no additional practice materials are required. These assignments give students hands-on experience with the theory while also serving as a modest grade boost.
Exams
The final grade is based on a composite score from the two midterms and assignments. To receive this grade, students must also pass a written exam covering the lecture material. Below are some example exams for reference:
Course Syllabus
Schedule
Lecture:
- Schedule: Wednesdays, 10:00 AM - 12:00 PM
- Location: South Building, Room 2-712
Note:
- Hungarian: Déli Tömb 2-712 (Interaktív tábla)
Practice:
- Schedule: Thursdays 7:30 PM - 9:00 PM
- Location: South Building, Room 2-502
Note:
- Hungarian: Déli Tömb 2-502 (Interaktív tábla)
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 Practice Score (PS) = Assignment 1 (50 points) + Assignment 2 (50 points)
Final Score (FS) = (LS + PS) / 2
| Final Score Range | Grade |
|---|---|
| > 85 | 5 |
| 75 - 85 | 4 |
| 65 - 74 | 3 |
| 40 - 64 | 2 |
| < 40 | F |
- Pass required on both LS and PS (individually) to attend the final exam
- Pass/Fail written exam from lecture material required to receive the final grade
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
- Bonanno, G. (2024). Game Theory (3rd ed.). University of California, Davis.
- Axelrod, R. (1984). The Evolution of Cooperation. Basic Books.
- Nisan, N., Roughgarden, T., Tardos, É., & Vazirani, V. V. (2007). Algorithmic Game Theory. Cambridge University Press.
- Myerson, R. B. (1991). Game Theory: Analysis of Conflict. Harvard University Press.
- Shoham, Y., & Leyton-Brown, K. (2008). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press.
- Christianos, F. et al. (2023). Multi-Agent Reinforcement Learning: Foundations and Modern Approaches.
- NashPy Documentation.