#
PřF:M7190 Game Theory - Course Information

## M7190 Game Theory

**Faculty of Science**

Spring 2012

**Extent and Intensity**- 2/1/0. 3 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)**- doc. RNDr. Libor Polák, CSc. (lecturer)

Mgr. David Kruml, Ph.D. (seminar tutor) **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**- Tue 14:00–15:50 M2,01021
- Timetable of Seminar Groups:

*L. Polák* **Prerequisites**- (
**M1100**Mathematical Analysis I || (**FI:MB000**Calculus I )) && (**M1110**Linear Algebra I || (**FI:MB003**Linear Algebra and Geometry I )) && (**M2100**Mathematical Analysis II || (**FI:MB001**Calculus II ))

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 6 fields of study the course is directly associated with, display
**Course objectives**- Basic course on Game Theory with the stress on applications in economy. Three basic mathematical models (normal form, characteristic function, extensive form) are studied. Various concepts of equilibria and their existence are discussed. Numerous practical problems are solved.
**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-our 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

- Enrolment Statistics (Spring 2012, recent)
- Permalink: https://is.muni.cz/course/sci/spring2012/M7190