M7190 Game Theory

Faculty of Science
spring 2018
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
Mgr. David Kruml, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Libor Polák, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 M2,01021
  • Timetable of Seminar Groups:
M7190/01: Wed 12:00–13:50 M2,01021, D. Kruml
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
After passing the course the students 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. Moreover, the students will be able to formalize practical problems by finding appropriate mathematical models and to discuss their equilibria.
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, multi-stage 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.
Assessment methods
A written exam consisting 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; one half is needed to pass the exam. Colloquium: one has to solve only the parts of exam problems or their simplifications; again one half is needed.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~polak
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 2019, Spring 2021, Spring 2023, Spring 2025.
  • Enrolment Statistics (spring 2018, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2018/M7190