M7190 Game Theory

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. David Kruml, Ph.D. (lecturer)
Guaranteed by
Mgr. David Kruml, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I || FI:MB101 Mathematics I || FI:MB201 Linear models B || FI:MB003 Linear Algebra and Geometry I
Basics of linear algebra and calculus.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 8 fields of study the course is directly associated with, display
Course objectives
The course provides an introduction to game theory and explains its basic concepts and results. Games in a normal form are studied more intensively, then the topic is developed to iterated and extensive form games. Furthermore, coalition games are studied. We focus on applications of the theory for practically oriented problems. This is reflected by a form of examination.
Learning outcomes
After passing the course the student will understand three basic mathematical models (normal form, characteristic function, extensive form) in deep and they will master various concepts of equilibria and their calculations. The student will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria. The student will get an intuition for ways how the players think, how the games could turn out, and an ability for detailed solving.
Syllabus
  • n-person games in normal form (equilibra concepts, their existence). 2-person games in normal form (antagonistic games, optimal strategies, solution of matrix games, games on the square, iterated games). Nonantagonistic 2-person games (bimatrix games, utility theory, the bargaing problem, threats). n-person games in characteristic function form (the core, its existence, von Neumann - Morgenstern's solution, the Shapley value, applications in economics). Games in extensive form.
Literature
  • G. Owen, Game Theory, Sounders Company 1983
  • Handbook of game theory with economic applications. Edited by Robert J. Aumann - Sergiu Hart. Amsterdam: North-Holland, 1994, 1520 s. ISBN 0444894276. info
Teaching methods
A classical two-hour lecture once a week comprising both the theory and practical problems. In the consequential seminar, further problems are solved, most of them announced in advance. More advanced problems are assigned to concrete students in advance. In 2021, the course will be given in online form and both parts will be recorded.
Assessment methods
A written exam consists of an extensive normal form problem and further two exercises concerning other types of games. Maximal numbers of points for all the parts of problems are given.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2023.
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