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PřF:M7190 Game Theory - Course Information

## M7190 Game Theory

**Faculty of Science**

Spring 2015

**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:

*D. Kruml*

M7190/02: Tue 16:00–16:50 M2,01021,*L. Polák* **Prerequisites**- (
**M1100**Mathematical Analysis I ||**FI:MB201**Linear models B ||**FI:MB000**Calculus I ) && (**M1110**Linear Algebra I ||**FI:MB202**Calculus 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**- Applied Informatics (programme FI, N-AP)
- Finance Mathematics (programme PřF, N-MA)

**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

- Enrolment Statistics (Spring 2015, recent)
- Permalink: https://is.muni.cz/course/sci/spring2015/M7190