Game Theory
Spelteori

FRT032F, 8 credits

Valid from: Spring 2024
Decided by: FN1/Anders Gustafsson
Date of establishment: 2015-02-10

General Information

Division: Automatic Control
Course type: Third-cycle course
Teaching language: English

Aim

This course is an introduction to the fundamentals of game theory. While originally developed to model socio-economic phenomena, Game Theory has recently emerged as a powerful framework to efficiently solve optimisation and multi-agent decision problems in engineering and computer science. After presenting the basic concepts from the theory of strategic form games, the course will focus on learning dynamics and their convergence properties. Particular emphasis will be placed on the study of network games, intervention and mechanism design problems, and more generally on applications of game theory to socio-technical network systems.

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• Have knowledge about the mathematical backgorund of iterated strict dominance, Nash equilibrium and understand the notion of mixed strategies.
• Understand concepts such as rationalizability, evolution and learning in games.

Competences and Skills

For a passing grade the doctoral student must

• Be able to use iterated strict dominance, and the theory of Nash equilibirum to find the equilibrium/equilibria of a game.
• Be able to formulate engineering problems as game-theory problems.
• Be able to discuss a game's structure and possible equilibrium/equilibria by the theory covered in the course.

Course Contents

1. Introduction to strategic form games 2. Existence of Nash equilibria, mixed-strategies 3. Potential games 4. Best response and noisy best response dynamics 5. Super-modular games 6. Population games and evolutionary dynamics 7. Fictitious Play and its variants 8. No-Regret Learning and Prediction 9. Bayesian Games and Information Design

Course Literature

Fudenberg, Drew & Tirole., J.: Game Theory. MIT Press,.
Most of the material is covered by the lecturer’s slides that will be made available together with pointers to the relevant literature on the different topics covered in the course.

Instruction Details

Type of instruction: Lectures. Most of the material is covered by self studies except the material on differential games where lectures are offered.

Examination Details

Examination formats: Written assignments, seminars given by participants
Grading scale: Failed, pass
Examiner:

Admission Details

Assumed prior knowledge: Good knowledge of basic math is assumed (calculus, linear algebra, graphs, elementary probability and Markov chains). All remaining concepts will be built within the course.

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page: https://canvas.education.lu.se/courses/28866